You should submit your B1/B2 visa page to show your current status in the U.S.

Yes, you can. USCIS actually asked one of my clients if he wants to do the same day oath ceremony before. You can definitely ask.

It could be an error on USCIS. Call them to check why they sent you another interview notice after green card approval.

P-1B or O-1B could be applicable. You should consult with an immigration attorney for more details.

You can give a try, but you will need more than academic degrees to get approved.

Yes, travelling within the U.S. is fine.

When an H-1B holder gest laid off, he or she should find new employer to petition new H-1B within 60-day grace period. Otherwise he or she should...

There is no limit. And you can claim your time outside the U.S. while on H-1B later.

Is this H-1B renewal? I would recommend you to consult with an immigration attorney to check how to proceed.

Your H-1B starts on October 1st. Check your I-94 to check your current status.