Nice screen name by the way. This is a big question! There are a lot of factors to consider when getting equipment. However, some of your questions are definitely answerable so I'll take a crack at those here.
First, I want to address your audio capture. Basically, you're on the right track. I definitely think that recording the bands that come in to play with a mixer is the way to go. This way you get echo-free and clean sounding audio. Better yet, in the most ideal situation, you would want to record each band member with a separate recording device so that you could do the mix on your own later and have full control over each voice and instrument. This would certainly cost more and requre more equipment and constant awareness of each recorder, but would definitely give you the most flexibility. Again, the more realistic situation is to record the band from a "house" or combined mix from a mixer. Another idea is to have the artists play with a click track that can keep them on beat to thier original recorded song. In this way, you can just ask for their produced album and use the professionally mixed song straight from the CD.
Going on to the cameras and editing system, I think you're all set to go with the three XF-100s and the Avid editing system that you mentioned. These tools should be able to get the job done in most situations. If you have three cameras and are still not finding the kind of shots you need after the shoot is over, you may have bigger problems on your hands! You'll need to speak with your cinematographers before the session starts and assign certain shots to them in order to be the most efficient. Even better yet would be to have a headset on so that you can talk with your other filmmakers over the noise of the band. This way you can give directions to them in order to avoid doubling up shots. Also, you'll want to speak to the band members ahead of time to see what kind of music they'll be playing and to familiarize yourself with it. Doing so will allow you to anticipate the beats.
Lastly, you definitely want to make sure that the band is comfortable having your shooters moving about the room. There's no way to get a variety of great shots unless you move the camera around the room so let your shooters be as mobile as they want to be!
Hopefully that helps!
P.S. Many editing systems come with software that automatically syncs your video with your audio in post. However, you'll want to make sure each camera is picking up natural, or NAT, sound during each session. Otherwise, the software won't be able to pair up your audio and video.