Do most people get to do their naturalization ceremony the same day in Newark, NJ?

Yes, NJ is great in this regard. It is one of the few places in the USA where that is actually happening.

It will take some time. There is nothing you can do really to speed up things.

I485

You would be better off calling them. Unlike USCIS, their customer service is not bad at all.

I need a lawyer about case pending 4 years

You can contact any attorney in NYC. There are many attorneys from the City who are answering questions here on AVVO. All you need to do is look.

Do I need an attorney to represent my case in reference to my brother's petition?

Yes. You surely do.

Can an illegal immigrant (entered illegally) abused by her illegal immigrant husband in the US for 2 yrs get any type of relief?

This person might be eligible for VAWA relief but the attorneys are correct in saying they need to review the facts first.

You might want to uscis.gov as a start point for your research.

What do I need to request my parents criminal and immigration records?

Nothing more than contacting the court where the record are kept as far as criminal records are concerned. Unless sealed, they are public record....

Is there hope once you got denied under section 212(a)(9)(i) for wrong information on the application ds-260?

There is always hope.

Any recent chnages made to h1b visa and also, if cap gap option for F1 visa holder still avialable

It might be. You should seriously consider talking to the employer who will be sponsoring you and their immigration attorney as well as your DSO.