If you overstayed your authorized stay before filing for asylum, the answer is yes. Staying beyond your authorized stay is a visa violation.

Yes, but it will be 16+ years before a visa will be available to you and you will likely have to go through consular processing.

Your son can apply for a student visa but it will likely be denied do to suspected immigrant intent.

You will not be able to change or adjust your status in the U.S. You would have to pursue an H-4 visa or immigrant visa through consular processing.

If you stayed beyond your authorized stay, the answer is yes. You violated the terms of your visa by staying beyond the period allowed.

You need to contact the U.S. Embassy for an update. The status could be an error. It could be a refusal. It could mean approval.

It is not clearly why you would falsely claim U.S. citizenship when applying for TPS. There are many issues with this case. You are back in the...

It depends upon why it was returned. Typically, you fix the error and refile. It may be a good idea to work with an experienced immigration attorney.

Your friend could look to take voluntary departure instead of an order of deportation. It is not clear if she is eligible.

You should work with an experienced immigration attorney to properly respond to the RFE. The best path forward will depend upon the specific facts...