no there should be no issues as long you use a DVI or HDMI cable to connect it, older VGA cables don't support 1080p
VGA supports greater than 1080p resolutions such as 2048x1536 just fine and I've used 1080p displays on VGA myself. Maybe some very old cables or whatever don't support it themselves, but VGA has supported it for years.
It sure does. Running 1920 x 1200 fine over VGA.
Good point about HDMI audio. Some AMD cards used to pass audio over DVI with the right adapter.