1) I know that 1080p TV's upscale 720p videos and games, but I've seen 1080p TV's display a 720p video with black bars on the top and sides. Why would it do that?
The TV was set at 1080p to its native resolution and is not automatically adjusted to fill the screen when lower resolution is viewed.
2) I'm going to be playing a lot of older videos and games, and was wondering if they would look better on a 720p TV, since it's a closer resolution, or a 1080p TV.
For video, upscale the movies according to whatever your scaler capable of. For games, set the resolution to whatever your TV's highest resolution.
3) Is it better to upscale 720p to 1080p or downscale 1080p to 720p?
I'm not sure if you can upscale 720p or downscale a 1080p. Best is to leave the resolution to its native.
4) Is there really a big difference between 60Hz and 120Hz? It looks like there is a bit of a difference but a lot of people say there isn't, and does 120Hz make a big difference for gaming?
If you have a TV with a 120hz refresh rate that is 1080p/24. The TV will display 24 separate frames per second; it repeats each frame 5 times within each 24th of a second in the case of 120hz. Here's an easy way to follow. Movie created on 30 frames per second viewed on 60Hz = twice as much frames of the same image is viewed on 60 Hz, which means it is 4X on 120 Hz. So a fast moving fast panning video will be sharper on 120 Hz.