First of all I'd like to know whether the IS is always active if it is switched on even when the exposure time in itself is short enough to guarantee a sharp image. I don't think the manual tells me about this. Will it inactivate itself when the shutter speed gets below a certain value?
It should always be active unless you have super steady hands or a tripod that negates any camera shake.
Is it possible that with a short exposure a simultaneous movement of the sensor (which is the type of IS in my camera) can actually prevent maximum sharpness? Not that it will create what the average viewer will call unsharp pictures. On the contrary. The image will look sharp within the expectation of most observers but can it be that without it in certain conditions a photo can actually be sharper than with it?
That doesn't make any sense to me. IS allows you to go shoot at several stops higher than you'd normally be able to accomplish. That means that IS steadies the lense/sensor and allows you to take shots that would otherwise have been blurred due to camera shake.
Now if you are shooting at a setting where you don't need IS, that presumably means that the effect of camera shake is negligible. If that is the case, why would IS cause any problems? The sensor isn't going to shake more than your hands would.
I might have just misunderstood your question ...
And will a photo taken with a tripod with IS always be (at least) as sharp as one taken from a tripod without IS or can a photo taken with IS from a tripod in certain situations be less sharp than when taken without IS?
Yes. Why wouldn't it be? If you're mounted on a tripod, you will not need IS so the IS will not kick in even if it's switched on.