basement in *extremely* uneven. I don't know a specific depth since I
haven't pulled up the carpet that's current covering it, but I would
guess some of the worst parts vary by maybe 1" over a 2' area.
......
How difficult would a resurfacing project like this be? I'm new to
flooring AND to concrete.

It's going to be a pain in the ass, no matter what you do.
How much headroom do you have to play with? The easiest/cheapest
solutions (well, after just sucking it up and living with
a bumpy floor, which wouldn't hurt you any) generally involve
piling more stuff on until the floor is level, but if the ceiling is
already at the 6'8" line, you'd be better off pounding the existing
floor out, and pouring a new slab. What sort of dampness/water
issues do you expect to have, how cold is the floor, and do
any sections of the floor move with the seasons?

And finally, will the fact that this is an interior surface alter the
estimated drying times? The room can be vented through a door into the
garage. What about fumes?

For concrete, it doesn't matter; it doesn't actually dry the
way you normally think of drying, the water chemically combines,
and it doesn't produce any fumes worth worrying about in
this context.

-Goedjn