I am sitting with my C/M in my lap and can confirm that the lens shutter closes when the mirror is pre-released.
It sounds like all your issues are relating to the lens itself. I've had similar issues with old lenses before---they stick and stop halfway, are slow to close, or stay stopped down after exposures---and a simple cleaning should be enough to fix all of these.
I have two of these bodies and for the longest time one did not work whatsoever. A shop wanted $250 to clean the thing, so I decided to just do it myself. It's actually really simple. BUT, and getting back to my point, the mirror lockup on this body has not worked for as long as I can remember and it has no impact on anything else, so I would bet the lens is the culprit here too.
If the release, mirror, and curtains of the body all seem to be moving smoothly and cranking properly, don't worry about it and just get your lens fixed.