Full screen:
This is with Pro, I don't think you can do it with the standard version, but there should be an option under 'Movie' for full screen or something and when you click on it, another little window should pop up with another selection for full screen on it. Click and you have a full screen Quicktime window.
I'm pretty sure that's how you do it, Pro's on my PC which is down at the moment due to lack of power (typing this on my iBook running on battery right now) and there is also a little text file you can make to make the movie always appear at full screen if you click on it, but that's on my PC too.
AVI's:
There is a plugin for Divx stuff for Quicktime, but most people use the VLC client of MPlayer, do a quick search for them, I'm kinda busy to do it for you.
Hope this helps.