I'm not sure if you can make auto-rename fully automatic (i.e. not even a single prompt) or change the rename format it uses.
Yes. There are several ways to enter customize mode but the quickest was is to hold Alt down and then click on the button you want to edit. You'll see a dialog with the buttons icon, command, label, and so on. Click the icon to change it. Check out my Toolbar editing tutorial to quickly get up to speed. (It's video-only; no sound.)
Yes. You can do it by type of drive or explicitly include/exclude certain drive letters. See the "Go DRIVEBUTTONS" command in the manual for full details, but if you just want a quick way to restrict it to some drive letters you can change the command from the basic Go DRIVEBUTTONS to something like
Go DRIVEBUTTONS=+cs
which will only show the C and S drives.
You can give lots of other arguments to tweak the command, e.g.:
Go DRIVEBUTTONS=fixed,-c,labels,lettersbeforelabels
That only shows harddrives ("fixed"), excluding C:, and also shows the drive labels but with the letters shown first.
If you really want to customize the drive-buttons (or just want to learn more about toolbar editing via a step-by-step tutorial), check out Gus's Triple Drive Buttons tutorial.