Is it ok to travel using a RENEWD National Passport as a LPR?

Yes, that is "OK". You will not have any issues.

I’m applying form I-130 for my brother. Do the supports documents and other forms need to be submitted with it? Thank you

Yes, submit all pertinent supporting documentation with that I-130.

I am currently on my F1 visa, do I have to maintain my visa status while my o1 visa is being processed?

Yes, it is best practice to do so.

F1 to H4 before marriage

Once again, cannot assume or expect that - will totally be up to the officer on whose desk your case will ultimately land.

F1 to H4 before marriage

Again, you cannot assume that - will totally be up to the discretion of the officer one whose desk your case will land.

F1 to H4 before marriage

To process the H-4 and H-4 EAD at the same time as the "Premium" case will be totally up to the officer on whose desk this case will land.

What is the better way/other way to change status from F2 to H4 in a month of H1B approval?

Don't attempt to apply for COS in the USA. You'll likely come to regret it if you do.

Complicated situation. Stand ready to have to briefly depart the USA and reenter with your still valid visa stamp - that's the "best case...

Am I entitled to any of my husband's settlement?

Not an immigration law question. I changed the category for you.

If charges were truly and in fact dismissed, then will have no effect.