The primary purpose of ADS is to control the 3 cost options of dynamic steering, dynamic suspension and sports differential. Of the 3 the latter is of highest value benefit, to the subset of owners whose driving style pushes the standard rear differential beyond its limits. The dynamic suspension is also good to aid such driving, although aftermarket suspension can be better, but it can also be used to soften the ride when best comfort is needed. The dynamic steering is the most subtle of the three because it changes the ratio. This makes the steering tighter in lively driving but can also make it much lighter for parking. There is also a fourth optional system affected by ADS and this is the braking guard part of the automated cruise control. This changes the activation sensitivity so that it is less aggressive in dynamic mode (which is quite important).
In addition to this ADS provides the option to change the shift points of the s-tronic transmission. As most S-car owners quickly realise, the points in drive are set really low and the car gets into the higher gears really quickly. This keeps the revs low and the engine sluggish. To get the car to move it is necessary to force kick-down. Fortunately sport mode exists with shift points set much higher to take advantage of the engine. ADS dynamic automatically puts the transmission into sport mode. But ADS can make the car much more sluggish. Comfort and Economic mode makes sure that gears 3-6 are used as sparingly as possible and the transmission will only grudgingly let go of gear 7.
The ADS setting in your photos (plus economic) have pre-set controls for the equipment. Supposedly Auto adjusts whilst driving but I never notice anything. Individual allows custom settings. I mostly have Individual set which is similar to Auto and just change to Dynamic when I want to drive fast. I select Comfort when I have "sensitive" passengers, and Economic when I realise that I really ought to have refuelled the car sooner.
In the facelift (2012) model ADS also changes throttle response in dynamic mode. To me this might be the only real benefit of ADS to cars which don't have the options. Also, as you have suggested, I understand that because the facelift model has electric steering, Audi was able to have ADS provide some variation in control of the standard (non-dynamic) steering.
As I hope you understand, the only thing that has been done in your car is to "hack" ADS - probably using the "green screen" engineering mode. Since this is a hack the results are limited. As I noted, with the button retrofit the functionality should increase, but without the optional equipment it will still be limited. Also note that the Kufatec kit in that link is for the pre-facelift model.