Yes it is safe to travel domestically with a pending I-589 and work permit. Yes, Hawaii, Puerto Rico, etc., are part of the U.S.

Yes, I have attended multiple asylum interview in the last month and they are going forward in their normal manner.

If you are not eligible for anything, you could ask for voluntary departure, or take a deportation order. Generally the next step is ICE will send...

Try filing 180 days before expiration. The processing time ranges from thirty days to about two years, and anything inbetween.

If you filed for a work permit under a different name, then the best thing to do is the refile it under your correct name.

You can show that you have rehabilitated from your prior conduct by showing 20 years without any further incidents of speeding.

There is no requirement to wait sixty or ninety days to petition for your father to immigrate to the U.S.

There is no way to know. It seems unlikely that having your bank account closed will impact your admissibility. But any activity you were doing...

You already filed the I-864? Whether or not you owe back taxes, the tax returns show your income and if your income is sufficient it generally will...

If you want to be perfectly safe, no. USCIS might deny your I-751 while you are out of the country and you would not be able to return.