a) whether this protein can be synthesized
In what way does is that a question? A protein is just a gene that get's transcribed by a ribosome. You can put that gene into least and let the yeast build the protein. The protein might kill the yeast and it might take a while to get the process streamlined but in principle every protein can by produced by yeast or some bacteria.
b) whether it can be efficiently extracted from nonhuman creatures
Who cares? It's not like we extract insulin from animals these days and we probably want the human version of the protein anyway.
c) whether removing it from a creature ages it, or if it can be replaced with no real loss.
Probably depends a lot on your definition of aging. It will take a while till the animal restores the blood levels of the protein and during that time amount of neurogenesis is going to be lower.
More interesting questions would be: d) What the half life of the protein. How often would you have to administer it to keep the levels in the blood constant?
e) Can you deliver the protein orally?
f) Are there processes that get messed up if you simply increase the levels of that protein? Does it increase cancer rates?
g) As the answer to f) is probably yes, is it worth it trade neurogenesis for a bit more cancer? Do you get enough bang for your bucks?
It will take a while till the animal restores the blood levels of the protein and during that time amount of neurogenesis is going to be lower.
But maybe when you're young, having it occasionally filtered would induce a higher set point for production.
Might be true when you're old too.
In experiments performed on mice, blood transfusions from young mice reversed age-related markers in older mice. The protein involved is identical in humans.
http://mic.com/articles/88851/harvard-scientists-may-have-just-unlocked-the-secret-to-staying-young-forever