Yes definitely your friend can go to the F1 status after the TPS expires, though he/ she has to be very careful on the grace period after the TPS. I know Sajha is the very good platform getting the information and it is very helpful though i strongly suggest you to tell your friend to hire a attorney for an hour which will roughly cost around $ 50 and ask all these questions. Also after the completion of the second master degree; they won't qualify for another OPT. I know how hard it is so i would strongly suggest to look for other alternatives if possible

Please correct me if i am wrong