MH also heals less I think.
But anyway, don't worry about picking up ALL of Satori's skills. Just concentrate more on ones you're going to -actually use-. Notably, most of her physical skills are crap, although a couple such as Fang Crush, Samidare Slash, and then ones that are sadly 1% skills, are fairly nice. You'll probably be giving her a staff anyway, but she can take advantage of the MP drain passive with a physical skill that way, still.
None of her elemental or support magics are a waste to learn, as they can all come in handy, depending on how much you're going to use her and/or chasers.
Parrar is perfectly fine for learning, too. Satori can't learn through, say, Little Legion, though, because then she doesn't get hit at all. Marionette Parrar is completely fine. Most of her skills don't have 100% chance to be learned, which might be why you thought it wasn't working. All the support ones do, though (Although most also require Charm, possibly other odd things, and as such are a thing to obtain)
As far what Satori should do whenever you put her in the active party, as far as random battles go, giving her Launch Earrings and poison boosting gear and spamming her Poison Art skill (learned via leveling, not blue magic) is a very stable, powerful, and mp-cheap way for Satori to be a very useful party member in randoms until like stage 13. And then she can just happen to pick up some other skills simply by being in your party as you fight!
