Piss easy, buy a can of carb cleaner, or 10k Boost (its a better carb cleaner specifically for Throttle Bodys) spray that in to the throttle body whilst you got the car revved at about 3000 and spray half the can in to their, and hold the rev like that to let it all circulate in the manifolds and clean as much gunk out as possible.
After that, once the engine has settled its revs back to normal, go for a 10 min drive.
That should solve the cutting out issue
And the sideskirts are a cheap replacement from VW ... the metal inserts love to rust, I replaced one of mine 3 years ago, and now its back to rusting again so will need to replace it soon.