They do not need to board the same plane. The children can come before the wedding, but not after the wedding.

She got her citizenship through you. She can file an N-600 for a certificate of citizenship.

I don't see why you could not apply for OPT since you are still in F1 status.

There is no national policy, it difference from jurisdiction to jurisdiction.

The children can be admitted on K2's. If they do not come to the U.S. you can file for them after you get married, or your spouse can file for...

You can ask for an expedite based on this.

Chances of an interview are high. Certainly CIS will notice the arrest and request information.

If you have proof of your pending application, it should be safe.

You do need to file that in order to change to an F1 or any other non-immigrant visa.

He cannot be issued the visa before it is available. You can check availability by going to the visa bulletin at the Department of State.