You did not explained what the officer told you at the interview.

Overstayed as a minor, now seeking to visit U.S. after almost 6 years.

You should consult with an attorney to review your case closely

My brother is a US citizen and plans to file i 130 for me and I am getting married in 2 months.

For the siblings category it does not matter if married or not

What action should we take in this situation??

Just wait, unless there is an emergency. You can send a letter.

How can I sign N600 Form as a father for my minor kid under 14 ?

They can sign it. Not a problem. Unless there is a physical barrier

It does not matter when you bring it up as long as you tell them

Cono puedo hacer para mi caso ?

Consulta in abogado inmediatamente. Tienes 1 año para pedir asilo lo cual es la semana que viene

I applied for marriage based green card, haven't received any notification from USCIS yet?

Have they cashed the check.? In any event, I would not worry until after 2 months

Is it required for all pieces of evidence submitted alongside the I-130 form to have handwritten signatures as well?

All forms must be signed by the appropriate party

Do we need a DS5540 now?

Yes. After February 24 2020 the public charge took effect