1. You should connect the PC to the HDTV using a DVI cable, if not then a HDMI cable.
2. As long as both video card and HDTV is HDCP capable (they should be), then either DVI or HDMI cable will display protected HD video content. HDCP does not apply to PC games.
3. Depending on your HDTV, it's resolution could be 1920 x 1080 (aka 1080p) or the lower 1368 x 768 (older standard).