1. No, it doesn't "average" the focus. When you expand the focus points, the camera uses the surrounding points only if the selected point can't lock focus.
2. Custom function for shutter and thumb buttons: these (many) choices let you customize how you want the shutter, AE lock, and autofocus to work. The most basic choice is this: do you want the shutter button to autofocus, or do you want the thumb button to autofocus (that is, pressing the shutter button simply fires the camera, with no AF.) Once you've made that decision, there are several other options you can choose, but that's where you start. (NOTE: in the choice you wrote above, the shutter button will NOT autofocus. So holding the shutter button halfway down does nothing except lock your autoexposure settings.)
Using the thumb button for AF is very useful. It means that I can focus on a static subject, then shoot photos, recompose, and keep shooting without messing up the focus. If the subject moves, just mash down the thumb button and keep shooting. (I usually leave AF set to Continuous.) I could go on and on about how great the thumb-button-AF is, but you'd probably get bored.
Other options: you get to choose whether the shutter button or the thumb button handles AE lock. I usually forgo AE lock in favor of Manual exposure mode or using the thumbwheel for exposure compensation. Also - and new on the Mark III - you can choose which thumb button does what. The Star button was the traditional choice, but Canon added the AF ON button, giving you several settings to mess up, er, choose. (Given that the Mark I and Mark II were exactly the same, and the Mark III changed everything, I think Canon dropped the ball on this one, but that's just me.)
Finally, you can use the joystick to toggle between a fixed AF point and the 45-points. Just pressing it once will toggle between them. (Not sure what the CF is for this, or even if you need one. Might be the default behavior.)
Does this help?
