Full-time MBA in campus during H1B/after obtaining priority date

USA H1B Visa
1

Can I go back to school for a full time MBA for 2 years on campus in a school in the USA after obtaining a priority date for my green card?
If I do this, my visa status would change to F-1? Can I go for F-1 after obtaining H-1 (dual intent) and purchasing a home in the United States?

If I do go into F-1 status, will I lose my green card priority date?

2

Your GC is for a future employment. You can be in any legal status while GC is being processed.

In fact you never need to enter into US to have a GC filed.