I'm not that much of an expert but:
HDR and AA are incompatible on certain cards I think- Nvidia maybe. I think this has been "solved" in the 8800 series though.
Depends on the implementation. Source engine games (Half-Life 2) support both HDR & AA currently, but Oblivion and Far Cry do not. Don't recall all the details, but the Source engine calculates things differently whereas the other two require hardware features that nVidia doesn't yet uspport. Iirc there was a patch released by ATI for Crossfire systems that allow AA & HDR in Oblivion, but I've got nvidia cards so can't say for sure.
HDR is hit or miss for me. Sometimes it looks nice, sometimes it's just distracting and I turn it off. It certainly gives my video cards a run for their money. I've got two 7900's running in SLI mode and even they can choke sometimes with HDR, AA at high resolutions.