You can use support skills in battle if you back out to that main menu type thing that shows up when you first enter battle, and it's either the X or Y option, I'm forgetful about it!
As for Alice, you mostly wanna keep one doll alive out of the ones she summons, and not kill it. For me, she summoned the elemental set thing, and I left the fire one alive so Mokou didn't take any damage for the most part, barring Alice's Last Spell/Whatever. Slice won't stop healing every turn, so you mostly wanna pile on damage to her and make sure not to hit the doll. If you do, try and do it with a Dark or Light Spell, they tend to take zero damage from those elements. After that, it's really a battle of attrition, I think one would call it. Just keep whaling on her and hope the leftover doll doesn't decide to hit someone like Patchy. Even if it does, you should be fairly fine, as Mokou's Last Word, will probably show up sometime. Just keep Sanae on healing, too, as Reimu can attack with her Light Spells and not harm the doll. You could also use Byakuren's defense buff on Mokou to see if it helps out with the physical attacking dolls, in case you wind up with those. I've only seen three sets: A group of Dolls with shields, and quite a few of them too. Then there was four elemental dolls, and then four regular blah dolls who died really fast to Sanae's move that was her bomb in UFO. I think they took like, 600 damage or something.
After figuring it out, I had an easier time with Alice. The super hard part for me was killing all those dolls and living through their attacks, so Sanae is still super helpful with her multi and single target heals. Just keep going, and good luck with it <3
This post was originally a lot longer, but I forgot I had to verify and lost all that. I hope what I said has some sort of aid <3