User blog comment:KodachiZero/Chain Chronicle V3 on the Wiki + Q&A/@comment-5957202-20161125013239/@comment-26432452-20161125053049

Yes, every time you use a chara on a quest they will gain some kind of affection that will raise his/her love point. The details are vague, but I think it will raise faster if you kill/use skill with that chara.

If you raise him/her love point to 10 then he/she could learn Deanju and use other arcana skill.

That favorite thing is just to show your friends who is you favorite arcana. To set it just tap your name on the blue bar below than tap the green button on 3rd row from the top, the one with heart icon on it and choose your favorite arcana.