VW 1.9L watercooled cuts out on low rev

[Tassie]

Hi!
I've recently been having trouble with my 1986 1.9L water cooled VW. It's been cutting out when I slow down before junctions and I need to restart with a lot of revs to get it going again.
I've looked on the forum and I know there are a lot of different potential problems with the air intake, carburettor and auto choke, but I am not that confident/experienced and feeling a little bit overwhelmed. I'm also on a deadline because as always it decides to break down just before we go away on a holiday with it, so I don't have loads of time to sort it out and it's my daily runner.
I've taken off the air box and the carburettor looks incredibly dirty. I've definitely spotted a hole in the oil breather pipe, which I'll replace, but it also seems like fuel has gone back through the air inlet hose towards the air filter. This filter looks dirty as well and was going to order a new one of those. I just have a feeling more is going on and I potentially have an oil leak somewhere as well. All the hinges/switches are covered in a layer of grime.
Before I put an order in at brickwerks, I'm wondering if I need to order anything else and if I can clean the carburettor without removing it and taking it apart (I have read that carb cleaner isn't a great solution). Any advice would be great. I am worried I have neglected some issues, but I am very new to this, so it can be hard to get the bigger picture and connect issues sometimes.
Thank you very much!

[TwinTurbo]

unfortunatly your images are not showing, 

what do you mean by fule has gone back through the hose to the air filter?

Does it do it hot or cold?
Does it drive well otherwise.

it's good to replace the air filter but it's not likely to be the cause of your issues.

Likely culprits are 

1) a vacuum leak on the vauum pipes including the servo pipe . block them and see if the symptom goes away.
2) the fuel dhutoff solenoid ( cylindrical item on the carb low down facing towards the back of the van, Plug and unplug with the ignition on and check it clicks .
3) Stuck autochoke, check the operation of the throttle and when warm that the choke is open.

Poor ingnition components can also lead to poor idle,  

[Stesaw]

Best bet would be a gummed up carb, bad or not connected vacuum lines / vacuum leak, bad dissy advance vacuum although more likely to be one of the others. When was the fuel filter last replaced? also, if you have a plastic fuel filter in the engine bay lose it and put one on the outlet pipe next to the fuel tank under the van.

The breather pipe will vent vapour into the air intake when hot which will over time leave oil in the intake pipe and the box.This might be worse if the breather tower has failed as well as they go bad, so might be worth replacing.

Where are you based? perhaps someone is close by to help out