1. Yes, I can confirm that your understanding is correct.

2. Regarding your new employer, your lawyers will provide the necessary assistance and guidance. It's important to note that in your current situation, the requirements differ from when you initially obtained your L-1A or EB-1C visa. At that time, you were required to demonstrate that you had the appropriate experience with the related company. However, now that you are in the AC21 portability phase, you are no longer obligated to fulfill that specific requirement.

You can recapture your H-1B time (one year) by requesting it during your next extension application. There's no deadline, and you might even recapture a full year if you exceed six months out. Documentation like passport stamps is needed.

If you are on a B-2 visa waiting for PERM approval. You can choose between:
Day 1 CPT: Allows you to work while studying but requires school enrollment.
B-2 extension: Extends your stay but may not allow work. Choosing depends on your work needs and ability to enroll in school.
Regarding your parents' visa interview, advise them to answer truthfully about your situation. Don't misrepresent information to USCIS.