I am using two partitions that I setup with LUKS encryption. Obviously, encrypted data is supposed to be written to them while they are unlocked and mounted...but...what happens if you shut down without unmounting the drive (though it will unmount during shutdown)and running:

cryptsetup luksClose

Is it still going to be encrypted, even though the luksClose wasn't run?

All data gets encrypted on the fly. LuksClose looses the encryption key for your session.

Thanks, that's good to hear.

Another question...I can't seem to find anything on changing the encryption password. There's lots of instructions on how to add new keys for the drive (up to 8, it seems) but nothing on changing the current key. Is it safe to say that this can basically be done by me adding a second key, and then deleting the first (original) one?

And if that would work...how does it go about changing the files that were already written to the drive? Or is it just stored in some kind of header to the file (which would be bad).

Bump......

Yeah. Each password that is added to the LUKS container is able to decrypt the contents.

So if you want to change your password you add a new key and drop the old. I would suggest to test the new key, though.