I don't see why you could not travel with an unexpired green card and unexpired passport.

Anything is possible. Why don't you contact CBP to have the I-94 fixed?

Sure. they could hire a private investigator, check public records, or perhaps there are other surveillance methods to use.

You do not need to be in status for your sister to file an I-130 for you. You do not even need to be in the U.S. But be warned that the I-130...

Yes, you can reenter the U.S. on an F1 and a current i-20.

If you are not a permanent resident or a U.S. citizen you cannot file a visa petition for anyone. if your sister is a U.S. citizen she can file an...

You could check the reciprocity tables for how to get a police certificate from Hong Kong. You are asking also if you can falsely state you did...

You cannot extend your status if you are not in status. If you are out of the U.S. you abandoned the application. So you can apply for a new visa...

If they did not cancel her visa, she should be able to visit the U.S.

The U Visa application and EAD should have zero impact on your H1b and i-140.