Hi from Slovenia

[NoHachi]

Hi Andre, nice find on the 800$ hatch.
Since your problem is clearly fuel related thats the first place I would check:
-Sometimes a near dead fuel pump can cause similar symptoms, particularly if the car has ever ran out of fuel and the pump ran dry.
-Check your fuellines: Sometimes when a shield is taken away, or the battery moved to the back (or something like that) the lines get to close to a heat source. This causes vapour lock and stalls the car after it gets really hot (stop and go traffic, trafficlights etc)
-Check the fuel pump relay: This is the most likely culprit. 9/10 cars that experience the problems you are describing are suffering from a bad fuel relay. Find a similar relay (same rating etc) from a newer car in the junk yard and replace..
-Dirty Fuel filter: Should be in good condition if normal maintanance has been applied. If in doubt replace immediately, might find some ponies hidden ín there as well.
-Check the ECU for fault codes. I doubt that it would be a ecu problem, these things are usually foolproof.

Edit: That rust problem you are having seems much more serious. You really should go and check out the complete underside of the rear. You'l be suprised how pourly designed that part of the car is and just how much mud and dirt can collect down there (I'm talking buckets full of the stuff).