Am I the responsibility of my sponsor { father } after 5 years of landing in US as LPR ?

As your sponsor he agreed to repay the government for means tested benefits you might receive. Depends if immigration enforces it.

Do I need to fill an updated version of my forms ( for example G-325A) if I found a new job since i filled my i 485 and i130?

You can update your information during your interview.

What should I do to get myself on waiting list(short notice interview) ? Pls tell me WHAT SHOULD i DO to be on such list?

Arlington Asylum Office 1525 Wilson Blvd. Mail stop 2500 Arlington, Va 20598

Yes you can travel within the US while waiting for your green card.

Need some advice on how to get started to make my husband legal

A dialogue in response to your request is not possible through this forum. Best to review the general information on USCIS.gov and then visit with...

I-134 for Haitian Reunification program was rejected? Filed on behalf the petitioner and Why?

Without seeing the submittal or the RFE, any response would be a guess. Best to visit with an immigration attorney and talk it through.

Is it possible & quicker to enter the US as a visitor after the wedding and start the I-130 petition and other forms there?

You will not get a visitor visa after you marry. You can apply for a K-3. Or you could come before you get married on a K-1, get married within 90...

Can I apply for working permit if my wife is a green card holder and we have a baby and my vicer has expired.

If the marriage is to a U.S. lawful permanent resident (green card holder), then the immigrant is in preference category 2A, meaning there are a...

It is necessary to file an I-90 and request a replacement.

Need Advice

Once you get your green card through your wife, you must wait three years before you can get citizenship.