They can reenter the US so long as they can explain the long absence to the US when they get here and show that they did not abandon their residency

Your new employer need file i485supplement j quickly so long as the job offer is a similar classification as your previous job.

You will benefit hugely from the services of an immigration attorney to help you navigate your petition. Not every conviction would disqualify...

You have hired an attorney who will protect your interest in this matter. Inquires to USCIS will be handled by your counsel

Be truthful in your application. I would say for arrest, it is a yes but for conviction, it is a no.

At this point the process server needs to seek substituted service. Opposing party needs to draft that motion and order and have the order signed

USCIS already have that information. You may also return to your prior counsel with this question and for information

See if you can make an appointment with USCIS to go into a field office and have your passport stamped with the parole document as an emergency

You should answer yes for arrest but no for conviction. You can provide documents to support your response

Yes. You need a new sponsor to file affidavit of support on the family's behalf and indicate that petitioner who was the original sponsor is dead.