Can the OL choose not to activate a monster during his turn (and for example to avoid Hex effects?)

I believe the OL must active all monsters. See 1st paragraph on the rules on page 11. Its says the OL must activate all monster groups. The wording gives a little bit of wiggle room to argue but I think the meaning is that you need to.

Know what? Nevermind. Rules pretty much answer the question...in bold. Yes, he has to activate all monsters. Guess this will be a random bit of information.