There is no requirement for you to change the name on your naturalization application. Your divorce decree should be sufficient.

Try correcting it through this email address [email protected]. Good luck to you in getting this done!

The message says your fingerprints were taken. That means that you went to USCIS and they took your fingerprints.

Yes, you can adjust status based on a U visa as a crime victim, or VAWA if you are an abused spouse, or a T visa if you are a trafficking victim.

It could cause a delay if you are filing a visa petition for your spouse, otherwise, no, it should not be a problem.

Yes, if she is still in legal, nonimmigrant status she can file for adjustment based on the petition her mother filed. if she has overstayed her...

Why don't you just file for a U.S. passport if the child is a derivative U.S. citizen? No, traveling on a foreign passport is not a problem.

Yes, maintaining lawful status is an exception to the one year deadline. Note that being in an abusive marriage generally is not a basis for asylum.

It is not likely that they will approve you with pending criminal charges It was very kind of you not to make any allegations against your wife. ...

There is an EOIR cover sheet you need, and you fee it in with USCIS and then file it with the court with a motion to recalendar: USCIS just issued...