If you are in F1 status, you need to stick with it even though you have TPS unless you want to screw it up everything . TPS is just an option but not any permanent status , it might lead to GC through marriage or employment. ( you need to consult lawyer) . But my suggestion is maintain your F1 status until you get GC. Best is to continue your study and new job . Good luck .

Dhakalji yo ekdum ramro prashna ho ani tapai lai tesko consequences ni thaha cha hajur lai jasto malai lagcha ra tapai le padhai chodne kura malai chai ramro lagena saayad majbur vayera garnu vako hola. @atomic ji le sabai kura vandinu vayeko cha tara ma pani yesma kehi kura thapna chahanchu:
TPS siddiyepachi athawa sakkina vanda kei mahina aaagadi college ko lagi apply garnu hola. Hajur le feri financial evaluation, sponsorship documents haru sabai pathauna parcha jato malai lagcha (tyo kura international advisor sanga garnu hola). Yes u do apply for F1 status with your school with the required application process (short and sweet vanna parda)
Next question you dont have to go to Nepal to apply. if your visa is expired and your TPS deadline is crossed and you havent received your I-20 then I think you might wanna go back to Nepal and do the application but if your status is good (TPS) so before it expires if you apply and get accepted and have i-20 in hand then u dont have to.
The only way to get your F1 status via TPS is by applying to colleges again. Remember TPS is not a status in itself.
** I am not a designated lawyer but these are the things I am sure but not completely sure about it. Hope that helps Mr/MRS dhakal ji