I can't get GLQuake to run. The one that came with steam insists it cannot *find* steam... O_o Winquake crashes hard, too. Got a download location?
fteqw ignores my -game command.

Corpses on platforms: I've not seen this on DP, so I'll have to find a GLQuake variant I can run for testing purposes. My suspicion is that the platform is somehow thinking the corpse is in its way (like a door closing on the player). It's dealing minor damage to it, then reversing its movement.
A cheap solution is to have platforms instagib corpses, but that's not very good. I'll need to find time and an engine that runs for me to look into it more.
To fix the bodies falling through the floor when you're standing in them... hrm. Again, I cannot reproduce because I'm using DP for now. You could possibly prevent the body you're in from turning solid again until you're out of it...?