hi.
high def monitors are just monitors that are able to
watch hd video,there is no tv tuner..
hd tvs are tv sets which are working as normal tvs, and are able to watch(or better to "capture" from tv tuner) hd video.
Yes. If the video input is 1080, then you will want a PC Monitor with at least 1200 vertical. A 24" LCD has 1920x1200. That's the starting point for "best overall LCD and TV monitor combo" display.