If a zone is burning , and you place a development, does it cause the burning zone to go back to 7 hit points?

No, once a zone is burning, it will remain burning. Putting developments adds HPs, but burning zones have no HPs to begin with, so while you can still play developments into a burning zone (Verena protection, Support that requires them, etc.), that's all it will do.

So far there is no way to heal a burning zone. They might create an effect that does that in the future but I don't think it's a good idea.