Absolutely, you should feel free to do this. There is no way to know if the judge will agree but if you provide documentary evidence, your chances...

If your wife is not working, then her income is indeed zero. What you should do depends on who is filing for adjustment of status, and based on what.

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.