I found a beautiful ring in a thift store. The stones appear real they are sitting in a setting that has openings on the bottom and sides so the stones can breathe. The setting looks like it is expensive. The stones look like citrine. The only marking on the inside of the ring is the word "Thailand". Could this be real gold?

It's basically impossible to tell with this information, take it to a jeweler.

Why would a stone need to breathe?

All real gold is stamped with the karat type... it's required. Doesn't sound like you have a precious metal.