He has no legal status. He is a person who overstayed.

An l2 is not required to spend any minimum amount of time in the U.S. and they can work wherever they want outside of the U.S.

She should leave by the date she requested, or file another extension application.

You can file any application you wish. The crime does not bar you from admission to the U.S. But no doubt the consular officer will consider it.

Your description sounds like a denial, not a notice of intent to deny. Yes, you should hire a lawyer and file the application again.

You could try filing a late-filed application for extension of status. Otherwise, they are out of status and required to depart the U.S.

Go back to the civil surgeon and request that they correct it.

The I-485 denial, by itself, does not disqualify a person from consular processing.

They mean the same thing. Normally in removal proceedings it is called termination, not dismissal.

If you naturalize, the children will not be included in the application. There may be a mechanism to bring them to the U.S. anyway, but generally...