there's no quarantine for animal when arrived here in Thailand. You just need an import permit and you can take out the dog with you. I know because I'm a pet shipper here in Thailand
Been to da nang few days ago, I only stayed there for few hours and back to Thailand, everything was so smooth. And no one also asked for my return ticket
No need. US passport doesn't require a visa here in Thailand. Lay over doesn't require a visa as well as long as you don't go out of the immigration ( depends on what country)
Just stay away in Thailand for couples of months. Just get more stamps in your passport from another countries. I think there will be no problem coming back here then