There are a couple of hotels that haven't reopened after Irma, yes. There are a ton of condos in Orient Village area that are just a block or two from the beach, good walking distance. Suggest you find an agent and get some recommendations for those.

As far as Jardin d Orient--definitely NOT walkable to the beach. It's actually a pretty fair distance to the beach and UPHILL. As far as bikes, no, I wouldn't do it. People drive VERY fast, the roads are not very smooth, etc.

Regarding internet, there should be a good connection, depending on where you're staying. Be advised that VERY few places in the Orient Village area have US TV, only French TV.

Regarding water, hopefully that situation has been resolved, but I haven't really heard much about it lately.