1. When / how do you get grevious wounds. Rules state, that "some terrible beasts" deal g.w. Do they deal this in general or only in certain circumstances?
Terrible Beasts with the Cruel nature deal grievous damage. You determine a Terrible Beast's nature the first time you encounter it (rules page 4).
2. Can you rebuild a Tower after it was destroyed? My guess is yes.
Yes you can.
3. Rules stare, when a tower gets destroyed, you erase the whole tower, except for the blackened spaces. Do they mean the spaces with an X? I couldnt find any blackened spaces in towers
I think that's a mistake in the rules. I went back and looked through and I couldn't find any other mention of blackening spaces in the tower construction grid.