The cost is the deal you cut with the seller - but I'm sure it would be much less than in the US. Just like when you buy a puppy back home, you can't really be 100% sure it's healthy - but you can look for obvious signs of illness - eyes, tongue, coat, lethargy. Thais love their pets as much as anyone else and purebred dogs are valued and babied (in contrast to the indifference with which soi dogs are generally treated). And the sellers at Chatuchak have their reputations to worry about. They return every week. If they sell a sick animal to a local, they can expect to have to make good on it and to lose a lot of face, and most of their customers ARE local. As for papers, I'm sure they're provided if the dog is purebred, but in Thailand you can never be 100% sure any such papers are authentic.
I certainly would head straight for a vet if I ever bought an animal at Chatuchak (or anywhere else, not just in Thailand). In any case you'd need to make sure it gets all the shots it needs to travel home with you.
As for carrying a disease back to America after petting one of the dogs, I'm certainly no expert but I'm pretty sure that's not possible as long as you wash your hands and clothes sometime before you return home. In fact, if you intend to pet any of the animals at Chatuchak, you should carry some hand sanitizer in any case. If the puppy sales area at Chatuchak were contaminated with parvo, surely all the puppies would be getting sick and some would be dying within a few days? And surely your dog at home is vaccinated?