1. Does IS mechanism reduce only the sharpness of a lens or causes any other type of IQ reduction?
The IS group is just a bunch of lenses, and so in principle it can suffer from all the same aberrations and imperfections as any other lens. However my guess from looking at the design is that internal reflections are the most significant effect. That would show up as flare and reduced contrast.
2. Is the IS reduction of IQ enough that it is visible to the eye?
It's not something I worry about. It's going to be a subtle effect, if visible at all. To test for it you'd need a pair of lenses with the same optical formula except for the IS group, and I'm not aware of any such lenses.
Looking at Canon's 70-200 lenses, the IS versions are both better than their non-IS counterparts. They are also quite a lot more expensive, and my supposition is that the price difference includes upgraded optics in addition to the IS. So in practice, from the customer's point of view IS actually improves your image quality because you are buying a better lens overall.