I can't imagine anyone more talented than you sir to address all of this. In fact, I can't imagine anyone but you addressing any of this to my satisfaction at all. Maybe you can, maybe you can't. But if anyone can, you can. I watch and wait.
That's an awfully high bar you've set! I doubt I'm the most talented to address all of this; there've been some very good books written on the subject (I can post a list if you'd like) and mine is ultimately just a 'layman' opinion. I might be the most committed (pun intended) but hardly the most talented.
In any case, I'll give it a shot, but I'll have to get back to you later. These questions obviously touch on several rather complex issues, and require a lengthy reply. I've written a good part of it, but it's a disorganized mess, and I'll have to finish and revise it. I'm guessing by tomorrow evening.
OK, I've given this some thought, and I might be able to enforce some brevity as I address your concerns. Feel free to ask for a more detailed reply concerning any part of this.
To begin with, your questions appear to organize into two distinct categories: (a) population control; and (b) sociopolitical arrangements (in particular economic arrangements). There is a unifying subtext here which is where I think I'll begin addressing these topics: resource availability.
The first key oversight I'm intuiting from your phrasing is the notion that whereas biomedicine will have progressed to an advanced degree far beyond the present, other spheres of endeavor will not have done so in a comparably revolutionary manner. With regard to resources, the foremost issue is energy, and the actual concern is petroleum. We already have the capability to halt our need for oil right now - with nuclear power as the alternative. The relative expenses are primarily transitional and what objections would arise are primarily aesthetic. But that we can do it if we need do it is not in doubt. Moreover, the prospect of a true revolution in energy production (e.g., cheap fusion) cannot be ignored. From an energy standpoint, we have the capability to sustain a population far larger than our own (and uniformly as consumptive as modern America) based just on our present technology. 30 billion is quite viable.
The ancillary concern is raw materials. In my guess, the three pillars of our future society will be: fusion power, genetic engineering, and nanotechnology. The third is the crux of this matter. The ultimate promise of nanotech is that we will be able to synthesize virtually anything we want. Well short of that, nanotech should expand our resource base dramatically in a number of sectors (the details of all that are a discussion unto itself). Indeed, molecular nanotechnology is one of the primary methods by which hypothetical rejuvenation (i.e., perpetual youth) will be achieved (the others include genetic engineering of self-sustaining bodies and restorative, regenerative medicine, with stem cell therapies as the most viable solution). In most scenarios, a world in which 'immortality' has been achieved is also a world in which nanotech has expanded our resources adequately enough to comfortably sustain a population of around 15-20 billion with a first-world lifestyle.
Turning now to your direct questions, we first have the specter of overpopulation. No matter how low the death rate gets, so long as a death rate exists, there is a birth rate to match it, and so long as every individual will sooner or later die, then that rate will be no lower than that matching a replacement rate of one surviving child per person. As we all now, amongst moder first-world peoples the birth rate has already fallen of its own accord below replacement. What demographic growth is taking place is because of immigrant populations from societies where this is not yet the case. Current estimates are that by the end of the next century, if everything continues much the same as present historical trends indicate the global birth rate will have fallen to at or below replacement.
The global population is expected to stabilize at between 9-12 billion people (and the latest estimates are at the lower end of this range). Assuming that fertility trends then persisted along the patter seen in wealthy non-immigrant populations of Europe, North America, Oceania, and East Asia, then the problem will eventually become not one of limiting births but of encouraging them.. One question at hand is: Well, if people live decades and centuries longer, what if they decide they want to have kids again? Yep, that is a good question.. There are several things to be said to that.
First, some number of people will choose to have no kids, or die before they get around to it. Their 'quota' if you'd like can be reassigned (or not). It's totally unknown how high this percentage will be. Going on the assumption that the problem won't resolve itself (i.e., that people of their own accord keep the birth rate at or below replacement once the population has matched limits deemed sustainable by whatever future standard) then one assumes that contraceptive measures will be heavily encouraged, if not mandatory.
It may very well be the case that (reversible) sterilization will become the norm. There is no scenario that I'm aware of in which technological 'immortality' has become available where totally reliable, totally reversible sterilization without any hormonal side-effects is not also available. It may then very well be the case that one would need to apply for a child-bearing permit. If so, then how that would be organized is up in the air because it depends on several factors, not the least of which being the type of political arrangements that are typical of the era.
In a political arrangement much as that of contemporary Western society, then I would imagine that everyone would have the right to one child, with unused shares alloted randomly to those who wish for another, with perhaps some minimum eligibility threshold for that. In a political arrangement such as that of present China, then the good graces of the Communist Party would probably determine who gets unused shares and who, if anyone, has the right to even one child. That's of course assuming this is all even necessary, and that the population will not remain below sustainable levels of its own accord or by less invasive methods (e.g., socioeconomic incentives). Keep in mind sustainable levels could be quite high indeed, especially if as I expect terraforming of Mars and Venus will eventually triple our living environment.
There is no reason why progeny should be restricted to any but the few. Everyone should be able to have at least one child, and if any people are forced to go permanently barren, that will not be imposed by resource limitations but will rather be a political decision, and can be avoided simply by not making that political decision. To the extent that barrenhood need be enforced by authoritarian methods, it can be done so via standard, reversible sterilization. Of course, one might ask what would happen if disaster befell mankind and everyone were sterile without the ability to reverse their condition, and to that I would say that the Amish would replenish the Earth (along with whatever other communities opt out of longevity - I'm sure there will be some).
This addresses your first three questions, I will get to the next four in a separate post. Feel free to let me know if you find any part unsatisfying; if need be, I'll backtrack after I cover the other questions you had.
OK, the remaining questions deal with sociopolitical arrangements, and in particular resource distribution (economic arrangements). As a reminder, these were the four questions as framed:
To begin with, let's just cut to the chase. The most rational solution to all these questions is en masse whole person emulation in a virtual world simulation on a sprawling quantum computing network - with redundant hardware, power supplies, and automated service techs scattered across the solar system and remote monitoring/operating capability from inside the VR. For all practical intents and purposes resources would then be limitless, and lifespans would be interminable, unless the virtual world were programmed otherwise. At the very least one could live until the death of the sun, if not beyond. What one would do with all that time is an excellent question, but I suppose one could opt to have the ability to sense boredom removed from one's personality.
I don't express this often (in order to conceal just how 'out there' I really am) but this seems to be the obvious outcome of civilization, and a quite viable explanation for why we don't see others galavanting around the galaxy. In a sense, it is the ultimate end of history, except of course that without dramatic psychological modification, which I think implausible (people wouldn't agree to be uploaded), novel threats and conflicts would surely emerge within the system. Hypothetically, we might be living in such a reality already; of course, if that's the case, then our programmers were obviously either deeply incompetent or quite malevolent, or this might be the aftermath of a dreadful hacking, or we may just be an artefact of a system designed to create randomized settings to be discovered far away from the home milieu of the original builders. Or we might be a virus. Who knows?!
There's no way to know, unless there were glitches in the system, and those would just be perceived as paranormal events in any case (if they were common enough, they'd likely be perceptually incorporated into the 'rules' of the system). My point is that a virtual system complex enough to simulate all the phenomena of the real world (assuming our world is 'the real world') or a close enough approximation would be indistinguishable from the real world, but if programmed accordingly would provide anything we wanted it to provide, including immortality and unlimited resources.
Anyhow, leaving all that aside, the first notion that we should dispense with is that physically 'aged' people in a society of perpetual youth (under our previous, more mundane scenario) will be socially 'old' people as we perceive them to be. For one thing, they won't technically even be aged in the sense that this conveys in present usage. A 500 year old will be potentially as productive as a twenty year old, unless we are dealing with issues of 'neural entropy' as we discussed before. In the event that we simply eliminated aging as we know it without any further rejuvenative intervention, you would also have progressive DNA structure deterioration (through random errors), and that would be a serious concern, but every scenario that I'm aware of that's been proposed for longevity also provides ready solutions to this problem (sequence the person's DNA at the outset and routinely correct errors).
So, getting back to the point, 500 year olds should be no less productive than they are required to be; in other words, they should be as autonomous and vigorous as a 25 year old, because physically and mentally they will be a 25 year old, just with a whole lot more stored in memory. We cannot predict what the effect would be of 'neural entropy' because we simply don't know how it would manifest, and it should not manifest until at least after a couple millennia under our current physiology. If people do become unproductive enough at about that stage that they must be supported by others, the support base should be more than adequate to support them under much the same arrangement as is currently in place, because 'attrition' should keep this population below around a quarter of the total.
Odds are that unless we are missing some critical factor this will be a non-issue. Moreover, a key part of the equation is just how much productivity is actually required of an individual. The more likely concern, due to increased automation and nanosynthesis, will be that there won't be enough productivity demanded of people. We are already seeing this unfold in 'post-industrial' society; we are already for political reasons artificially elevating the degree of productivity required of workers as a whole (though hardly anyone frames it that way). In short, the overall trajectory of technological advance suggests that our lifestyles will become dominated by leisure rather than industry. What we will do with all that, who knows? A lot of people 'don't know' how to do much of anything else. I guess they'll just have to find lots of hobbies..
Which brings us to the fourth question above. There are two things to be said to that:
(a) While I think society is likely to stratify based on length of life lived, from a physical standpoint everyone would be a coequal of everyone else. In other words, it would be as if the world were filled with twenty-somethings, just some of the twenty-somethings had been around a whole lot longer than others. Past the first century, they'd be all but indistinguishable; our 700 year olds could pass as 100 year olds just as easily. This assumes no further social compartmentation, which is a very dubious assumption to say the least (it'll happen). But, to the extent that that will happen, it will be because that's what people as a whole want to have happen, not because it must happen.
(b) In contemporary society most of our lives are governed by the demands of child raising (contrary to popular opinion, this wasn't always the case, especially for men, but that's another discussion altogether). This would obviously change. My view is that self-indulgence would naturally become much more of a priority - to the great consternation of the more Puritan-minded among us.. I guess people would do with that whatever they felt would make them happy. I know I could happily spend at least a couple hundred years moving around the world myself. The final answer to your question though is that a "society dominated by geezers" in this case would hardly be a massive nursing home as the phrasing suggests, but more like an extended yuppie happy hour. =)
People have always managed to find things to occupy their time, and ennui is hardly a more awful prospect than drudgery, which humanity seems to deal with well enough when need be..
Going back to the first question, it's not entirely clear what kind of power you're referring to: political, social, economic? Historically, people have wanted power because it leads to prosperity - fame and fortune - and also the often unstated reason (frequently unacknowledged by the 'powerful' even to themselves) of sexual mastery over oneself and (perhaps more importantly) over others. It's unclear how much of a motivator this will be in a future society; the benefits of power have already broken down and are breaking down further in Western society. Modern civilization is in the idealized sense a civilization of universal empowerment. All of our sociopolitical institutions are oriented in that direction, and to the extent that they fall short, it is due to resource limitations. At the very least one would expect that the urgency of securing power would be reduced in a society of millennial lifespans.
One obvious solution, if this is actually a problem, is term limits, and term limits can be implemented across an array of endeavors if necessary (not just the political sphere). So, by example, in another hundred years, you might be told that you've been a lawyer long enough, and it's time to actually go find something positive to do with your life! ;^) But, I don't really think it'll come to anything like that myself. By comparison to the present, the future will likely be both socialist and individualized. That's just the way it's likely to be. All of this is determined by resource limitations, and as practical limitations are steadily reduced, the outcome seems inevitable over the long run.
I think I'll just stop here for now and see whether I've adequately responded to the issues you've raised. BTW, the most difficult question of all, that you did not raise, is what if longevity is expensive, and not universally available. That is a whole 'nother can o' whoopass there..