I can't say for certain about how to do the faith quest since it's been a long time. But I believe you need to see faith having sex with the two dudes first before you can continue it. Once you do that, you'll be able to talk to her by using the right code (Sorry I don't remember, but the wiki might have the correct portal code), resulting in you ending up in the past to decide whether or not to warn her. You'll have two options after that which will result in different endings.
As for the npc that randomly appeared, that's not part of faith's quest. Her name is Irene and she's an assistant that can save you once per hunt if you're caught by the ghost.