Do thwy take strays

It depends on if it is a cat or dog. The fees are listed on the website

Yes they do but if you have had the animal for over a week they consider it your pet at that time I think it's like $75.00

Thier dogs if found no owner will be moved around from shelter to shelter to find home if noone finds them there. And odds are they will be taken.

The puppy I got was a 2 month old stray!!!

The answer is yes depending on dehavure eval

Yes. But if someone doesn't claim the dog they will put it down/kill the dog. You're better off seeing if the dog is chipped at any vet office Petco PetSmart to find the owner, put up a picture on straydar on Facebook. Even use the neighborhood apps. Posters