Some skill that are unlocked thought the loyalty tree are more than 100, which is the max. Can I increase some how or is my game gliched?

You get loyalty from having them do task, I'm pretty sure there isn't a cap.

For some reason the developer used "loyalty" to describe two separate UI elements. There's the loyalty bar which determines how fast  obedience drains, and the loyalty "skilltree" which unlocks stuff. In my opinion even if the developer plans on deprecating the loyalty bar, the value for the "skilltree" should be renamed submission because it's a bit comical to be speaking of loyalty when you're just talking about someone's willingness to take it up the butt.