Rush skill quest - party composition?

Thank you.

And an even stupider question: do you have to have the Indecipherable Book in hand before you talk to Manji to initiate the quest? Or does the book drop from the tauros you kill inside?

If it's the first case, where does one get the book?

You need the book before talking to him. Storybooks unlock quests that lead to skills. The book drops from the Tauros in the SW Dungeon (or buy in FM).