yes, All AF-S lens will work with D80, And the monopod/tripod problem is really depend on what shutter speed you can work on, But it is better to have monopod/tripod when taking indoor/lowlight conduction because you can boost the ISO high enought on the D80 for a faster shutter speed

Yes, the D7000 has a focusing motor in it as well so it can take both lenses w/ motors in them (like this 70-200) or without (like the 80-200). The D70 also has a built-in motor so it will work with both as well. The D7000's AF system is much more advanced, however, and is very quick in comparison to my D200's AF, fyi.

The sample image was taken w/ this 70-200 VRII and my D7000.

Personally, I wouldn't recommend that simply because you're gaining very little by putting on a teleconverter on the 70-200 lens when shooting sports. This lens is ideal for action that is happening closer to you. By putting a teleconverter on it, it makes it a little unwieldy to shoot with. That is when you will want to use a super telephoto lens (300mm and above). That is best for shooting subjects that are far away. Also, by putting the teleconverter on the 70-200, depending on which one you use, it will also decrease your effective f-stop accordingly. If you're shooting night sports, you're going to have a tougher time trying to stop the action and get good results. Best to leave it as-is and shoot it at wide open at f2.8 and enjoy its capabilities as originally intended. If you can't afford a super telephoto at the time, at least try renting one and see how it works for you. You'd be surprised at the results you'll get!