-I-539 should be filed by your family memeber who wants to be H4 holder, not filed by you. Your employer will file I-129 for you and the I-539 had better filed concurrently with your I-129.
Q1. For the Q3g in Part 4 about employment experiences, Do I need to report my Curricular Practical Training (CPT) experiences? These CPT experiences are indicated in my I-20s, though.
Q2: I also got an invitation to work for another school.
-You can work part-time using CPT EAD for another employer before t=your h1 is approved.
Do I need permission from my primary H-1b employer before I file my concurrent H-1b?
-Confused in your current status, F1 or H1?