The answer is "no" on the I130. To be in proceedings a person must be served an NTA. Notice to appear. The person need not appear in court, see an...

File for an EAD extension if eligible. Good luck.

Follow up by case specific inquiry using receipt number.

Your mother must become a USC to petition for you.

I am unaware of any restrictions for undocumented persons from enrolling at universities.

If you are single your LPR mother may petition for you to get a green card.

You may be eligible to apply for naturalization under the 3-year rule.

What specifically are you applying for? You wrote "I applied for my case". This is vague or overbroad.

No. Your stepchildren when admitted may petition for the biological mother. Good luck to you.

It's better to address it now. Inform USCIS and Consular office of error. Best of luck to you.