It's possible. Some people may hazard to guess. We will have to wait to find out.

There is no rule against it. In the past in such cases, CBP would insist you come to the airport and they would put you in removal proceedings. ...

Yes, you could do it that way if you wish.

You can put your Canadian address on the application.

You should be prepared to answer questions about it.

Five years from the date he became a permanent resident. Unless he is filing based on marriage to a U.S. citizen, in which case it is three years.

No doubt the officer must adjudicate your I-751 first.

You can simply apply for a passport. But for a naturalization certificate you file an N-600.

They should back date your permanent residence to the date you got asylum.

Follow up with customer service. If that fails, then file a petition for hearing with the federal court.