Clogz, thanks for the link. I've answered my questions with it and several others.
I got the self timer to wind. Actually, it was not so much a wind as just moving it. It hadn't been moved in years, so it needed a little more push than I originally thought was prudent.
HP, P, and LP are programming modes that involve the camera setting the aperture and the shutter together. I don't have the right lens, so it makes no difference to me now.
Indeed, the f-number should show in the viewfinder, as well as the exposure comp. and the program mode. They don't. Maybe the circuit is bad.
Exposure lock cannot be off'd or changed without turning off the exposure lock.
The little LED window is battery check that is activated by pushing the on switch all the way over.
Are there other Contax users here? I don't see any mention of this camera in the archives.