Nick, i gave you advise about the sat nav before including helping you fit one.
They are all interchangeable. The 16:9 screen will work with all MK computers (only MK4 is DVD), and the 4:3 unit can work with both versions as well. Each MK 4 DVD computer has a firmware (which can be upgraded). You can even modify the GUI which I have done in the past. If you JUST bought the tv screen, it would only function as a radio CD player (and yes the alpine could still run off it). I think you may be getting confused tho. It cannot control your climate control. The CC unit gets relocated to where your storage tray is (above the heated seat and ASC+T button).
However, sneakily (and not a lot of people know this), the 16:9 screen wired up fully (to sat nav and cluster, etc) can remotely start your car and cool it down at a given point in time (or warm it up). Say if you were to leave your dog in the car at the supermarket or whatever.
The ETK/TIS Cds cover all of BMWs range, you just load the software onto your comp (compatilble with XP), you can then part search or type in the last 7 digits of your chassis number and your vechiles details will appear. You can fault find and it gives you all the information you need to service your car (inlcuding the dreaded injector replacement!). I've got loads, primarily because you cannot get a Haynes manual for the 330d/320d.