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.
In a nutshell, this is what is wrong with "immortality".
Those three make sense. However I suggest a fourth (unless it's already covered by nanotechnology) -- a reliable source of fresh water. Unless we can perfect something that can affordably convert sea water to fresh, we may hit a barrier to future population growth.
Also, I think your essay is good enough that you might consider posting it as a stand-alone thread.