Is the Fallout Script Extender compatible with steam versions? I'm very eager to try mods like the Wanderer's Addition, Enclave Commander, and Real Time Settler but i don't want to screw up my install.

Yes. You just install it as per usual and run the game through the FOSE loader rather than Steam.

Would I still be able to run the game without FOSE if I wanted to?

yes

Not if you want to play the "Enclave Commander" mod!

Of course. FOSE is an addon with it's own launcher, you're not required to use it if you don't want to. Just start the game from the default launcher instead.