My German is very limited, but, yes. It looks like that yoga mat is made of EVA foam, which is what people use when they make their armor out of Foam. Just make sure one side of the mat is plain with no texture.
Sometimes yoga mats can be made out of a lower density EVA foam and they sort of fall apart as you cut them. It would be difficult to know this unless you actually tired to use it, unfortunately. Have a look at this post from Kamui Cosplay who is in Germany for some of the suppliers that she uses. A little Cosplay Shopping Guide
Yep. I use yoga mats for bulking out areas that won't be visible and need some extra padding to have a proper fit on me. They do tear if stretched too far and aren't great for structural elements in my opinion but they do have uses and are a cheap option when stuck for alternatives.