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.
The embarrassing answer is that for hundreds of millions of years the world was gay. This was a terrible time for evolution, and the fossil record is quite pornographic. Not only that, but reproduction was very difficult. It's believed that the dinosaurs died out as a result. Then a miracle happened, and females appeared. The rest is history.
[Source: Secret archives of Darwin Central.]