Joking aside,the first thing I'd say is that if all this has started since replacing the clutch and DMF,then that's the cause of the problem,and it's the mechanic's job to sort that out.
All of the problems there would fit with the clutch plate not moving correctly on the splines,and if,as you say,the splines are ridged and mushroomed,then they sound either worn or damaged.
If you google gearbox shaft splines,you'll get a very good impression of what they should look like.....elongated teeth as on a gear but longer,and smooth down their sides and top.
They should not be ridged,scarred or obviously worn.
If the shaft is completely free of grease,that may also lead to the clutch plate sticking.
I can understand a little bit of grease from the centre of the clutch bearing,as long as this hasn't got onto the clutch plate itself,as this would also knacker it,but it would slip rather than judder.
Was this done at an Audi dealership?....if so,drive it up there,park it and complain loudly in the showroom until it gets sorted....failing that,a phone call to VAG customer services may also concentrate a few minds.
I appreciate that the most likely cry will be one of wear and tear,but a splined shaft is not expensive,and is pretty easy for them to replace,but the point is they should have noticed,and informed you,rather than giving you back a car that doesn't quite work.
This picture isn't great,but it does show the shaft I think you're talking about,running into the box,and it isn't ridged or damaged.