Today I see the drive-side crank here is loose on the spindle. The
non-drive side moves a much smaller bit, that appears to be the bearing
play (it could probably use new bearings anyway).

I never much got into bicycle mechanics really, so what [special] tools
would I need to get this thing apart, and what kind of crank is it
exactly? (to get a replacement, if it can't just be tightened up,,,) \

The spindle is a tube that runs almost all the way through from the
drive side, to the non-drive side....

http://www.norcom2000.com/users/dcim...s/loose01.html