Can a person apply for naturalization after 2 years of denial of naturalization?

Your sister needs to discuss the reasons for denial in a private consultation with an immigration attorney to obtain an answer.

The children are not allowed to attend school in a B2 visitor status.

Applying I-130 while h1b extension is pending. Is there any impact on h1b process and stamping?

It depends on how you proceed. Please discuss the specifics of your case in a private consultation with a qualified immigration attorney to obtain...

Transfer from f1 to f2

It sounds like you have some timing issues. Please consult privately with an attorney before filing anything.

When can I switch jobs during an EB2-NIW application?

You need to share the details of your case in a private attorney consultation to get a useful answer to your question.

I864a. Can my parents who do not live at my principle residence act as sponsor to help me meet requirement for income?

No, they are not household members but they can file a separate affidavit of support as a joint sponsor.

WHAT FAMILY NAME I SHOULD USE IN I - 485

Your new married name is what you should use.

Got an RFE for my H1B transfer in premium processing. Not yet resigned from my current employer. Is my H1B still valid?

Yes you're current H1b is still valid if you continue to work for your current H1b employer. The RFE does not change that.

My I 131 was filed in sept 2013 and it is almost July 2014 and my I 131 is still in acceptance stage after 10 months.

Just give it some more time and continue to follow up if you don't hear anything.

Just answer the question about relatives. The question is not asking about friends or acquaintances.