Pursuing Masters on F1 Opt , COS filed for F1 to H4/H4 EAD

I am currently working under F1 OPT which will expire on July 9, 2020 and will be filing for COS F1 to H4/H4EAD in next week. I am planning to pursue second masters under F1 that offers Day-1 CPT courses to continue the employment till visa status gets changed to H4. Can I continue my masters after changing visa status from F1 to H4? And will I be eligible to get work authorization after getting H4 EAD and continue my masters together?