Thanks for your replies, in advance.
If life here is a zillion-to-one chance, why are there so many different species of plants and animals?
The second part has nothing to do with the first. (Sounds like a push poll question.) The diversity is explained by inexact reproduction and differential survival.
Do plants and animals share a common ancestor?
Yes. The cladistic structure including both show at least one common ancestor.
All living things take in "nourishment" and excrete "waste". Why?
It't actually due to the second law of thermodynamics; one cannot extract all the energy in food. Something is left over.
What could possibly explain the origin of the "instinct for survival"? Doesn't this imply a priori knowledge?
There is no "instinct for survival." Species that do a poor job just die out. It's like the Texas Marksman joke.
You ask some very good questions. One I happen to know the answer to off the top of my head is, "Do plants and animals share a common ancestor?"
One of the oldest known animals are anenome's which voluntarily move to capture food. While these animals in many ways look and behave like plants, it is their voluntary motion which makes them animals. You would have to look even further back to find the shared ancestors of plants and anenomes.
I don't know exactly why there are only two sexes instead of three or more. Sex is basically the exchange of genetic material which has the advantage of producing more diversity so two sexes are enough to accomplish this.
Did they evolve simultaneously?
Basically yes. However, that didn't happen all in one step. The first organisms that exchanged genetic material were hermaphrodites so they could be both, male and female. Only later some species became sexually "more specialized" by dropping the female function for one half of its population resp. the male function in the other half.
This is only a quick and dirty description but if you need more accurate information on this topic I'd recommend PatrickHenry's list-o-links. Maybe he can point you directly to a website where this is addressed in more detail.
I see three semi-independent questions here:
1. Why is sexual reproduction advantageous?
2. Why only *two* sexes?
3. How did the two sexes arise from non-sexual ancestors?
To address these, some common misconceptions need to be cleared up.
First, sexual reproduction does not actually require two or more sexes/genders. Sexual reproduction, fundamentally, is just the exchange of genetic material between two (or more) organisms. These organisms don't have to be "male" or "female" in any sense, and in fact many single-celled organisms (e.g. yeast) engage in sexual reproduction by fusing two separate cells, exchanging DNA, then separating.
The second misconception is that specialized male and female forms had to arise at exactly the same time (and *poof*, all at once). They didn't.
So to put it all together, the rise of sexual reproduction as we know it today in animals (and remember that many plants also engage in sexual reproduction, including male/female specialization) could easily have come about through progressive stages such as:
1. Unicellular organisms which reproduced asexually (i.e. by simple division), e.g. bacteria.
2. Unicellular organisms which gained the ability to fuse and exchange DNA in addition to division/budding, e.g. yeast.
3. Simple multicellular organisms (little more than communal colonies of unicellular organisms). Any single still would still have the ability to reproduce (and thus spin off a new colony) by either budding or two-celled sexual exchange. For example simple molds.
4. Simple but more advanced multicellular organisms, where different cells in the "colony" gain the ability to become more specialized based on location or chemical environment. Some regions would become specialized for ingestion of food, for example, while others would become more specialized at sexual reproduction (including specialized gametocyte cells, as well as simple "genitalia" or reproductive sites). Reproduction via single-celled division by any cell would become lost and the organism would now either entirely or primarily on on sexual reproduction (although the gametocytes would still in theory have the option of reproducing asexually). E.g. the higher fungi.
5. Full-blown specialized multicellular organisms as we know them, with specialized organs, etc., with a heavy dependence upon sexual reproduction via specialized organs, and a specialized differentiation between the "donor" and "receiver" cells involved in pairwise sexual reproduction at the cell level (e.g., "sperm and eggs"). At this point the organism is technically hermaphroditic -- there are not "male" or "female" forms. Instead each individual has the anatomy necessary to both donate sperm and produce/nurture eggs, and sexual reproduction involves a bi-directional transfer, with each of the individuals both donating and receiving sperm during the "sex act". E.g., earthworms.
6. From step 5 it's a relatively straightforward step to specialize into two separate sexes, *one at a time*. For example, a mutation could lead to a subpopulation of individuals which have lost the ability to donate sperm, but still have the capacity to produce eggs and have them fertilized. This subpopulation would not die out, since it could still reproduce by being fertilized by the remaining hermaphrodites in the population. Thus it is feasible to have a viable population consisting of a mix of hermaphrodites and "females", without specialized males yet existing. Or it could start in the opposite direction if the first "mutant" subpopulation involved individuals which lost the ability to produce eggs, but still had the capacity to fertilize the remaining hermaphrodites (i.e. "males"). At this point the "specialists" (that is, the "males" or "female" subspecies as the case may be) would be expected to specialize even further in become better DNA "donors" or "receptors", and this would create a genetic "arms race" which would be likely to cause members of the remaining hermaphroditic subpopulation to eventually specialize into the "other" sex, although that could take a lengthy amount of time. But the point is that it needn't arise overnight to "match" the appearance of the "first" sex, as might appear at first glance.
As for *why* sexual reproduction (i.e. why couldn't life have just gotten by for several billion years asexually), there are various forces at work. The first is that the "shuffling" that takes place during DNA exchange produces vast amounts of new variation, far faster than occurs during asexual reproduction. This buffers a species against being wiped out by various challenges, such as environmental changes, a new predator, a new disease, etc. The more that the individuals in a species resemble "clones" of each other, the more they can *all* be felled by a single adverse event which they are all vulnerable to in the same way. With higher variation, statistically many individuals will by chance be less susceptible to whatever adversity strikes the population.
Also, evolution takes place much faster in species which reproduce sexually than in those which reproduce asexually (for a given generation time and birth rate). In a sense a creature that reproduces asexually is its *own* "species", since it doesn't interbreed with any others of its kind. If beneficial mutation "A" takes place in one asexual bacterium, and beneficial mutation "B" takes place in the bacterium right next to it in the petri dish, those two beneficial mutations will never come together, not even in future generations, in order to make a "doubly blessed" individual. But in a species with sexual reproduction, *all* the beneficial mutations that occur in *any* individuals have the potential of being "shuffled together" in a subsequent generation in order to produce individuals which benefit from *all* of those beneficial mutations. Evolutionary "advancement" is greatly facilitated. (And even the creationists who claim not to believe in "macroevolution" should be able to see how this still helps to make beneficial "adaptation" vastly more efficient.)
So through a variety of effects, species which acquired sexual reproduction (with or without separate sexes) would be expected to "outevolve" those species which had not. And as you look around, you'll note that indeed most "complex" organisms reproduce sexually (including plants), and even unicellular organisms frequently do so or find a way to achieve similar outcomes (e.g. "lateral transfer" of DNA in unicellular organisms).
Why two sexes instead of a world of hermaphrodites? Presumably because having specialized males and females opens up more possibilities for more efficient functioning by each. Also, have a two-sex system *enforces* sexual reproduction, whereas hermaphrodites can often "fertilize themselves" -- which combines the worst aspects of both sexual and asexual reproduction with few of the advantages.
As a sidebar it's interesting to note that some animals (which ordinarily reproduce sexually) still retain the ability to reproduce by "simple cell division" at times. Through a process known as "parthenogenesis", females of the species produce a diploid egg cell which is a "clone" of its own DNA, and female offspring are produced without any fertilization by any male (a true "virgin birth"). Animals which can do this include some species of insects (e.g. aphids), fish, amphibians, and reptiles. And apparently a kind of half-assed parthenogenesis has been found to occur in domestic turkeys.
Why *only* two sexes? Probably because while there is a direct route for the production of specialized male/female forms from hermaphroditic beginnings, there doesn't seem to be any obvious way to produce *three* types, nor would there be any obvious advantage to doing so (and several obvious disadvantages).