USCIS transferred my case (I-485) to my local USCIS Office for further processing

Each petition has a receipt number. Check which one the Service's letter refers to - I-730 or I-485. There is nothing wrong with having both...

At the interview for adjustment of status,do me as the immigrant need my birth certificate? What if I only have my passport

Yes, they will want to see your original birth certificate. Alternatively, if you can't get one, they may request other documents such affidavits...

Do I need to wait the result of my application for extension of stay before I leave US?

What if there is an RFE? (Request for evidence). It happens pretty often. Who will be answering questions and providing additional evidence?

For the Immigration Service there is always a record. I don't think, though, that you will have a problem travelling.

Would it be problem at a time of getting citizenship?

There should be no problem as the misrepresentation was not material - she would have gotten her green card anyway. For naturalization, however,...

If you are a US citizen your spouse should have been forgiven. Immediately hire an experienced immigration lawyer.

VAWA

There is no time limit, check your center for processing times. men can also file I-360 - everything depends on the circumstances.

Can USCIS call for 2nd interview if we file 1447 (b) on a delayed naturalization case?

They have 120 days to adjudicate your petition from the day they received your response to RFE. Whether they will call you for an interview...

Relocating before green card interview

Immediately after relocation file AR-11 and by separate letter the Service Center where you filed your petition. There shouldn't be any delay but...

Hello. How long will it take for I-130 to be approved??? Please help.

If you have proof that Service received the petition (Notice of Receipt) relax - there is no way to expedite. Count on 7 to 11 months.