In film cameras with film advance levers, what happens if I don't crank the lever all the way? Will the lever 'remember' the last position it was at and keep the shutter button locked until I crank it the rest of the way, or will the film only advance half a frame and I'll double expose half of the previous frame?
It depends on the camera. Most 35mm film cameras (especially more "modern" ones :) do two things when you wind on - they advance the film roll by a frame and they reset the shutter curtains to the start position. My last 35mm film camera (a Praktica SLR) wouldn't allow the shutter button to be pressed unless I'd fully wound on. However, there was a button I could press while winding on to disengage the film-winding mechanism: this would result in the shutter being reset but the film left in place and could be used for double exposures.
My Konica FA-something from about 1980 remembers, and only lets the shutter fire again when it's fully re-set (as others said).
I can pull the lever completely in one motion, advancing the film 1 frame and fully cocking the shutter, or do it in several smaller steps. I think that is called single stroke advance. Some cameras (older, i think) have double stroke advance, like some early leicas.
It's possible that some older cameras (or cheaper, newer ones) are less sophisticated, and require you to be more careful not to accidentally double expose a frame, but it depends on the make/model of camera.
ps - current disposable film P&S cameras have this kind of protection, FYI.