@jyure I believe @neerman answered most of the questions.. But I would like to point out one thing. TPS is not a status so you will still have F2 as your status. And F2 visa does not allow you to be a full time students. This is something you will have to talk to school on how to approach it. And if you do need to change your status to F1 even with TPS or may be they will allow you to take full time classes as F2 with TPS.

I say this because for F1 with TPS, students are allowed to take less than full time classes after letting the school know that you are on TPS & also work on EAD but they do have to follow every other rules for F1. But for F2 the rules are opposite which is they are not allowed to take full time classes. So I would confirm with the school.

@neerman please comment if you know more about correlation between F2 status and TPS status.