After a couple of weeks, it seems that the stalling issue is finally resolved. The car does still drop to 500RPM when braking with the clutch in, but this doesn't cause it to stall anymore.
However, when the A/C is switched on, the car seems to not be running smoothly. It is fine most of the time, but when sticking to a constant speed/revs, it feels like the car misses slightly. It is not a missfire or anything really bad, but it just doesn't feel smooth. I checked the air filter and somehow there is only one bolt holding it together now. Both of the rear bolts are missing the nuts below, so the air filter box cover is only resting on the bottom half. I'm not having much luck getting new nuts to fit, but I have yet to take it apart completely to see if I can repair it that way.
The strange thing is that the non-smoothness only happens when the A/C is on. With the A/C off it runs fine.
Apart from fixing the the air filter box, any other ideas on what to check that may be causing this?