F2 to F1 in process, husband's H1B approved.

I am currently in the US on F-2 Visa. My husband is currently on his STEM OPT. I have a query regarding my current visa status. I have an I-20 from University of Notre Dame for Fall 2020 and have filed COS from F2 to F1. (Receipt date: 05/20/2020) My husband's H1B has been approved and will start from October 1st. I haven't filed for COS to H4 as my COS to F1 is already in process. The University allows F2 status holders to atudy part time.
1. So, considering my current situation, can I start studying part-time on F2?
2. Will I be out of status from October 1st? or can I stay and study part time as I had filed my COS early? Does this come under authorized period of stay?
3. Do I also need to file COS to H4? Can two COS applications run parallely?

Your reply will be highly appreciated.