For Quest 07 you finish the quest by going back to the shrine, sleeping, and then selecting no bedmate. The ghost will show up again and now you can officially recruit them as a devout :) This is as intended, because you have the opportunity to recruit before the day officially ends.
For the wings: is this by any chance what you saw? https://ibb.co/Wx8Nw4r
This is the On the Defensive skill that you receive when you recruit Maggie Fairbright, and gives you an extra 5% HP for the remainder of the battle, but there shouldn't be anything in the game that would activate that skill on its own. The demon has about a 90 attack power, so if your def is low it would have taken out a huge chunk of that when it attacks?