Can you like be a pet foster parent to see if it works out? I really just want to see if there are any allergic reactions before adopting.

That I'm not sure about. Don't see why not though.

Very few let that happen,first to experienced foster pet parent of own dogs of rescue dogs, not many would accept

Our adopted dog, Diesel, was a prior adoption that was returned because he didn't get along with the family cat. The shelter took him back. While they place some animals in foster homes, those homes and no kill rescue shelters are established foster care that the NYACC frequently uses. If you choose a pet from them and it doesn't work out, they'll accept it back but you're likely to not get your adoption fee returned.