I would say answers to every other non-immigrants status will equally apply.

If we need to fall back to any visa status , that we currently have, after end of TPS period we need to satisfy requirement for that particular visa category ,during TPS period , whether F1,F2,J1,B1,B2. If we violate terms for any visa category during that period we need to start from zero for any new visa category.

The thing is period of TPS can vary so it might be worthwhile hanging onto TPS category and enjoy benefits , if you have another path to PR/Citizenship. I am supposing here that you are pursuing after PR/Citizenship.

If we understand TPS(Temporary Protected Status) it will make much clear regarding what it is protecting against and term temporary. Temporary: It is temporary for the term defined. Protected: It is protecting us from not having to leave US ( so no deportation, even for someone out of status and who filed TPS) , and while not-leaving it is giving facility such that we can work and feed ourself. In addition, it is providing protection for entry to US through Advance Parole during the temporary period.

Our other responsibilities or facilities doesn't change.

I hope this helps.