If you have a general question about immigration law, you should post it. But if you want individual advice what to do in your case you should...

There is a discretionary 60 day grace period.

There is not enough information provided to answer your question. Find an attorney licensed to practice law and show them the papers.

Since it takes about a year to process there is not likely to be anything new until about December or later.

You do not need any permission to work outside of the U.S. for U.S. company.

You might want proof that you have been living together also. As well as shared experiences and intermingling of assets.

You can file for a change of status to B2 within sixty days. You can also get a new H1b petitioner even after that without being subject to the...

He can come and apply for a refugee travel document.

It seems to me that the J1 does not allow "dual intent" so that if you are an intending immigrant, you would not be qualified for admission as a J1.

Most likely they will give you a request for evidence to show you got the remaining shots.