If I sent my poliwag to the day care center till it was level 25 then gave it the water stone would it evolve into a poliwarth?
No, only Poliwhirl evolves into Poliwrath with the water stone. However if your Poliwag is over level 25, you can still level it up one and it will evolve into Poliwhirl. THEN you can use the water stone.
I don't think so, I'm 99% sure that you would have to evolve it into a Poliwhirl before you can evolve it into a Poliwrath.