I find myself buying scrolls every time I can, but I have never bought a book before. Do books do anything else besides providing lore?

They increase monster knowledge and can provide information for sidequests.

I i'm guessing that knowledge about a specific monster makes it easier for you to kill them? What about the Runes of Power books?

Is that the I, II, III, and IV ones from Chapter 3?

Those are keys to a sidequest's puzzle.

I cant verify this in any way, but sometimes it felt like Geralt knew somethings in dialoges that he only could know if he bought the books. only a feeling though, so I dont know if it really changes anything buying books (except monsters)

Yes the knowledge does come naturally but you have to kill a lot of monsters of that particular species before you gain all three levels. I gained 3/3 for harpies this way.
But for the bigger ones oyu need to go for the books as there so few of them.

And as to the OP's question , besides the lore , books let you know the best tactics for a monster, like using fire against wraiths etc etc...