it will play a video file with a resolution of 1920x1080 (1080p) fine its just it will look like its too large for your display. just play it full screen and it will be downscaled to 1280x720 (720p)
Not quite. It should be downgraded on the fly to whatever you screen resolution is.
If your screen is set at 1680 x 1050, it will shrink down the 1080HD film to fit, not enlarge the 720HD version.
DVDs are at 720×576, so there is no option but to scale them up. Which is why they look rubbish if you're too close to the screen. But a 1080 HD film will be slightly scaled down, with no loss of quality.
You can always take pixels away and maintain quality, but you can never add them.