I feel weird about bumping this old thread, but what about her Enneagram type?
If we're strictly talking about her music, (or, if we want to get more exact, her lyrics) I find that she's pretty Six-ish. As noted above, her music is very others-centric, which fits in with the "stands up for friends" part of Six. It seems to take a while for Hayley to let go of her relationships (as shown in "All I Wanted", "Stop This Song (Lovesick Melody)", "All We Know", etc.) And Sixes are also very protective of their beliefs- and she's stuck with Christianity despite all her doubts ("Turn It Off"). Plus, just the fact that she had these doubts (probably against pressure from family and friends) screams Six. "Playing God" also shows her hatred for people making decisions for her.
Also, look at this text from enneagraminstitute.com:
(bold is my own text)
"When moving in their Direction of Disintegration (stress), dutiful Sixes suddenly become competitive and arrogant at Three ("Misery Business", "Feeling Sorry"). However, when moving in their Direction of Integration (growth), fearful, pessimistic Sixes become more relaxed and optimistic, like healthy Nine ("Born For This", "Looking Up", "Where the Lines Overlap")."
So I think she's probably a Six. As for wings, Five doesn't really seem to fit, but I find that she's often pretty anti-Seven. Listen to "Never Let This Go", "This Circle", "When It Rains" and "Misguided Ghosts", all of these songs criticize running away from your problems. So I'll go with
6w5 6 with balanced wings.
Then again, I'm no expert on the Enneagram so I may be totally wrong.
As for MBTI, I agree with INFJ. *nodnod*
Edit: My gawd the size of that post. I really need to get out more.