1. You probably will still need a cable box, it depends on your cable system.
2. You will have black bars left and right, and on some analog (SDTV) shows black on all four sides. Stretch modes work, but personally I don't like just horizontal stretch. Both 480i and 1080i need to be de-interlaced. If the electronics do not de-interlace well, picture quality will be degraded.
3. There are no interlaced LCD monitors currently being made. Interlaced LCD's are not totally out of the question as they could be used to de-interlace 480i and 1080i, the previous field's scan lines stay on the screen until changed, resulting in a de-facto "weave" de-interlacing.
4. Computer video cards sometimes have refresh rate selection, primarily for CRT monitors where going above 60 fps (60 Hz) reduces flicker for some people. LCD's may or may not accept a higher refresh.
Video hints:
http://members.aol.com/ajaynejr/viddoubl.htm