Could it be something to do with the automatic choke, sounds like it could be faulty, no idea about the cranking though sorry

 

Dont know if this will help but here goes, I had a mark2 golf gti that did something quite similar. It would rev it self when stood still and cutout sometimes.

took it to once place and they said it was airflow meter, (£150 second hand)decided for a second opinion

The second garage spotted the problem, a warn washer !! cost 2p !!
they replaced the washer and re-timed the car ....total cost was £20!

The washer was rubber and and had worn away, i may be worth having a look
around your engine for signs of wear ?

just a thought ....

Good luck

 

Hi mate my a3 was doing similar to that a few months ago, i got a garage to plug it up and it turned out to be the teperature control sensor. Just thought id mention it if it helps.

 

also its worth checking the various vacume pipes, epecially thoues runing to the throttle and any to the MAF sensor, if these are split or leaking they will cause poor idle, cutting out etc. had any warning light came appeared on the dash?