Key!
#3
Depending on the year of the car it may have to be programmed to your car too. That is an additional programming fee from your dealer. Most 01 and all newer Audi's need the key programmed to the cars immobilizer system.
#5
You could still have immobilizer, the transponder is a simple pill inside the key that wouldn't be effected by water. Whatever electronics there are to this are encapsulated inside what looks to be a glass container. It looks like this, not a picture of your key but you get the idea. If you turn the key on, look at your dash lights, if you see an icon of a key on your dash panel mixed in with water and oil pressure lights etc, then you do have immobilizer.