Can't really say because I have no idea which card or PC your talking about.Generally I would say yes it does.Almost every card these days has either Mini-HDMI port or a HDMI port.
Depends, since there're quite a few models. My MSI card came with HDMI port, but no DVI-to-HDMI adapter (only DVI-to-VGA). You have to look at the specific model on the manufacturer's website, they'll have the list of ports there.