Are we allowed to use Event Moves on battles?

I was also going to ask about Move Tutor Moves but I figured out the setting hasn't changed in that if I'm correct.

We can use Move Tutor learned moves from the games, but, on the other hand, The Move Tutor Shop is just for the moves Pokemon cannot learn in the games by Move Tutor. It's just a little confusing, and I want you to confirm this.

I even have a new Pokedex book now and it's even better than my last one.