I simply want to be able to assign actions to keys in different locations on the keyboard, other than F1-F12. Is this possible? How?
Yes, you can edit illustrator keyboard shortcuts by going to the Edit menu and selecting Keyboard Shortcuts (near the bottom of the menu). From there you can create your own set by clicking the "Save" icon to the right of the dropdown menu (see pic below). Navigate to any command using the options below that to assign and save your shortcuts.
Also, because this is a little unclear in illustrator: the way you assign a shortcut is by selecting the space in the shortcut column to the right of the command you want to edit, then just typing the shortcut you want to assign (shift-command-M, for example). Illustrator will alert you if there is a conflict.