Leaving the U.S. with advance parole does not trigger the unlawful presence bar.

You could try. File the waiver and indicate it is for conviction of a crime, even though you deny there was any such conviction.

Yes, put the PO Box as the street name instead of a street name.

Bring your medical exam to the interview. Make sure it is not expired.

Sometimes CIS pro-actively locates people who fall out of status. Other times they do not.

Yes, you should be able to file a lawsuit against your affidavit of support sponsor to sponsor you, even if you have chosen not to work.

Yes, you can file an extension of status to get your full six years of H1b status. I don't understand your question about whether an employer can...

Submit your transcripts and evidence you have paid this year's tuition and are currently enrolled.

If your visa and passport are not expired, you should be able to return to the U.S. on your H1b visa.

It depends on the location. In some places there may be immigration consequences. In others there will not.