Hi and welcome to the forum.
You didn't say whether the car was a k-jetronic or a digifant, unfortuntely mk2 gti's are well known for poor idling. Just look on any forum and there'll be loads of people with the same troubles.
I'll assume the car is a digifant, the first thing to check is whether there are any air leaks in any of the vacuum lines (don't forget the brake servo lines). Another likely candidate is the idle stabilisation valve, this is a little metal cylinder that lives above the rocker cover (with breather pipes and an electrical connection) remove that and give it a good soak in some carb cleaner. Also measure the resistance across the elctrical terminals should be a reasonably low impedance (10's of ohms ish). Other things to check are the idle screw seals and stuff like that. Cleaning out the throttle body can also work wonders.
The water inside is most likely to be caused by one or more of the following:
Damaged/missing door membrane between the door card and the door.
Leaky door seal.
Blocked sunroof drain channels.
Good luck
Tobz