You can remain as long as your status is valid. Visas have nothing to do with your ability to stay in the US. Visas are only travel documents....

Do I have to file i-944 for my parents because I'm sponsoring their Green Card with i-864 form ?

Yes, your parents must each file form I-944 to meet the public charge guidelines. Good luck.

My sister applied for green card in F4? how to get I-130 Inventory for India till March 2012?

Go to myproritydate.com to get the best estimate which is probably 5-6 years.

Is there a way to help my father if he has a ice hold ?

You need to get your father's complete criminal and immigration files and consult with a Board Certified immigration attorney immediately. good luck.

H1b withdrawn and reactivated after 45 days?

Yes, you get another 60 day grace period. Good luck.

Applying Green card for my parents?

You should NOT do anything until they have been in the US for 90 days. Once you file the case, after the 90 days, a travel permit will take about...

Is it possible to convert h4 to h1 without having h1 stamped?

Yes, you can change status in the US if your petition was filed requesting that action. Why do you not ask your immigration attorney this question?

You will have to have your nieces declared orphans which is so difficult but not impossible.

You can travel but you abandon your pending cases and cannot return. I am sorry.

You need to consult with a Board Certified Immigration attorney and and not discuss this on a public blog. Good luck.