Help with thinly slicing garlic
For the general case of cutting vegetables, I will always recommend a mandoline. Cutting with a mandoline vs. knife is like drawing a straight line with ruler vs. without - even though very experienced people can get good results both ways, using the mandoline is always quicker and more precise. And for anybody whose fine motoric skills are compromised, the mandoline adds even more value than for the average person. 

But the main disadvantage of the mandoline is that it doesn't work so well with the "butt" of the vegetable. With a normal-sized mandoline, I usually start using the cap when the food is worn down enough to pass about 4-5 cm above the blade, and because the cap is fiddly when the food is too thin, I leave the last 1 cm unsliced. There is no problem with making paper-thin slices of something large like an apple; but I would be wary of slicing something smaller than a garden radish on the normal mandoline, and wouldn't attempt a single garlic clove. 

The small garlic mandoline looks like it is designed to solve this problem, as a video of it shows that you can push it down inside a holding "cell" instead of having to rely on a nail to hold it in place as with traditional mandoline caps. But it might still lead to large butts (which you can of course process as per Kate Gregory's answer). 

Another thing important about a mandoline is that it should stand on a surface by its own. Mine has a rotating frame in the back which lets it stand stable on the counter, like a tablet holder. I only have to move the vegetable while the mandoline remains stable. Some have holes in the bottom edge so they can be put on a bowl rim. I can't see such a mechanism in the one you linked. If it requires the use of both hands (hold it stable with one hand while slicing with the other), its usability will be diminished a lot, especially when you have trouble with muscle coordination. You should try to find a model which can stand stable on its own. The person in the video does not use such a mechanism, maybe you should write to the manufacturer and ask if it exists.