The fee listed is 350 for puppies plus a $75 deposit to neuter puppy...once puppy is old enough does that cover entire cost of neutering and also does it include any shots puppy will need? Basically for $425 what is included?

I think they only charge $15 for their vet to do the first shots

Okay so if the dog is already neuter, it's just a flat $350 fee. If not, like you said you would have to pay an extra $75 but you'll get it back once the dog is neutering. As for shots, when adopting the dog they will give you a paper that indicates when the puppy will get their shot. I'm not entirely sure if they cover the first few or not (you should call and ask) but I know on adoption day it's just $350 of neuter and if not then it's an additional $75