I'm not 100% sure, but you can look up hardware-related IDs in your device manager. Right-click Computer (7) or My Computer (XP) -> properties -> hardware tab -> device manager. One of the tabs should have a drop-down list of several IDs you can write down.
As for killing the graphics card, dunno, man. I would just block the vents and wait for it to overheat and auto-shutoff, then unblock the vents and start it up again and see if it worked.
Yep, any information available can be found in device manager - expand the display adapters section, double click on the grapics card listed there, and then go to the Details tab.
I'm not sure which, if any, of the details available are unique to a particular card, though. Possibly Hardware IDs, Physical Device Object Name, or Matching Device ID. There are also Install Date and First Install Date fields, but I'm not sure how reliable they are - the first install date of my card says 04/09/2011, when I know I first installed it in August 2010. The install date says 20/11/2011, which is when I last updated my drivers.
As for how best to make it malfunction, stress test sounds like the best option, yeah. 3DMark might do it, or there are probably other programs around if you Google. You could also consider overclocking it for a little while, but doing so voids the warranty, so if they find out you did so, then you're screwed.