You should answer the question affirmatively given information provided.

Yes the brother may apply for a visitor visa while i130 is pending.

I agree with my colleagues about form N565.

You may begin the petition by filing for form I130 through consular processing. Consult with an attorney for guidance.

Yes you may petition for your mother despite her overstay.

Yes you may use the previously issued A number.

No wait until decision by USCIS as you won’t need to apply for I751 if approved.

No this must be disclosed in the N400 application.

Best to review form instructions for guidance.

May be best to have an attorney review statement.