There is a rule that all Federal political apointees must submit letters of resignation to the new Administration ...

[getagrip_already]

2. Nor is the potus forbidden by law to fire them

As long as they aren't civil servants, they serve at the pleasure of the president.

They were appointed that way, they can be fired that way.

Yes, some positions require senate confirmation, but not for firing.

The PG is different however. Only the board of governors can fire the PG.