I think all of the options have their own points, but I think You makes the most sense. After all, before you can know others, you must know yourself.
Also, the focus on their relationship feels like it might have slightly better odds of Azula going on a date with Ty Lee. Failing that, it also seems like it might result in Azula finally spilling the beans about the loops.
As for the other questions, I think it's worth remembering that Mai and Ty Lee don't just lose their knowledge at the start of the loop, they also lose their perspective. While they could probably easily answer the question at the heart of Your Father, I don't think they could do it coherently enough to get through to Azula until the very end of this loop and there's no guarantee that a new loop, with a different focus, will take them on a similar enough path or get them far enough to give her the answer she needs until the very end.
[x] You. Princess Azula the Blue. Heir apparent to the Dragon Throne. Conqueror of Ba Sing Se. Half Roku—half Sozin. Where you are, so is the Fire Nation in all its rapacious glory. Yours is the blood and bone of empire. All the things you should have ever wanted to be. But sometimes you think of fire dancing under the Moon; of three girls and the horizon and a flight across half the world. Is that wrong? Are you wrong to dream—to think, so briefly, of being something more?