1. External temp - Check the external temperature sensor and make sure it's in the right spot. "The right spot" is actually on the passenger side brake cooling duct. If you look at the cooling duct there is a hole somewhere in the middle (looks like a male/female connection). Alternatively you can try swapping the temperature sensor. It could just be faulty.
2. "Speed" button - This shows the average speed, period. It can't show you the "acceleration speed" because it's not programmed to do so. Unless there's a special version of the E36 OBC somewhere out there....
3. Range - Range function is based off your consumption. That's how the OBC calculates it. Your consumption when you start the engine shouldn't differ much from right before you switch off your engine. I can't think of a reason why it would change so much.
If you need more information about the OBC, check out this link.
http://www.waddekao.com/files/loafer/obc/obcmanual.pdf
Good luck.