Do any of you know if they test all the animals especially kittens/cats on the Parvovirus?

Yes

Test them for what? Most animals are health checked most dogs are temperament tested.

Panleukopenia is the feline equivalent to parvo. They have full vet services at the shelter and run tests but keeping your pets up to date with shots is the owner's responsibility. To directly answer your question, the shelter would not knowingly adopt out an animal that was sick without informing the adopter and ensuring they could care for the animal.

I think they do