It may take 3 to 5 months for an extension to be approved. You must wait and be patient.

Where can I submit the petition paper for my parents? At what address?

Refer to the form instructions on USCIS webpage for direct filing location.

That appears unusually long given date of submission. Contact USCIS for further guidance.

Can I submit the I-130 and I-485 at the same time?

Yes if your mother is in the US, having legally entered and you are over the age of 21.

You may but your associations with possibly inmates may be an issue for future immigration matters.

How to expedite form I 130 process time? Is there any other alternative available to obtain interim visa till I 130 is processed

Unfortunately expedite requests are generally not resulting in actual movement on cases.

Is my foreign divorce valid in the USA?

Yes your divorce should be legally valid in the US if legally valid where divorce was done.

Yes this will likely be reflected in your background check.

Documents for citizen application and take with me in the interview?

You should bring your GC, BC, passport, divorce decree, any criminal docket sheets, and all other relevant documents.

Incorrect amount check sent for i-539?

US CIS will return your forms and request correct filing fee.