You would only be able to stay in the U.S. if you filed a Form I-485 before your status expired. This is not likely to happen given the information...

You need to dismiss the removal proceedings. You should work with an experienced immigration attorney.

Overdue taxes does not prevent you from being a sponsor.

You could. Be prepared to answer questions about your trip, have an itinerary, and have a return ticket.

Your mother-in-law’s unpaid medical bills should have no impact on your application for a green card.

There is no set timeframe in which your status will change.

You be able to enter without issue. You should travel with proof the charges were dismissed.

You can travel if you have a valid advance parole document. Whether that’s advisable depends upon more information about your case.

It may be possible to change back to H-1B if you have time that can be recaptured. You could apply for EAD based on your spouse’s approved I-140.

Cases are adjudicated on their own merit based upon the officer assigned.