There is the encyclopedia in Sanahtlig's toolbox where I've tried my best to decipher the moonrunes so that you don't need to.
And yes, that is what Karin does, but it should be noted that the CD on her damage cut is long. And one turn is more than enough... most of the time. It's an interesting combo with her Charm skill - other damage cutters can get horrendously fucked over by an unfortunate Charm proc, but Karin needs two to get screwed. Regardless, in general you want a damage cut on a short CD instead, as such skills only matter when used against Overdrives.
Furthermore, the usefulness of Hime are measured in their debuffs. Karin only has Blind and Charm. While extremely potent ones that Thunder has little access to (Rami-Rami only I think?), Thunder is so very starved in the Atk/Def debuff department that it makes fitting Karin into a team tough.Oh shit, I didn't even notice. Fixed.