Just continue doing the Fey storyline (check the Fey lead - click on the envelope icon in the top-right of your screen) to earn her trust.
Unless you mean increase her heart bar equivalent? Right now you can't - she's one of the Faction leaders so her progression is going to be a little unusual :)
You currently don't. Just progress with the other leads. At some point they meet at the church, if you check all the options after completing all the three storylines they will merge.
