Hey, the Crucifix is used to prevent the Ghost from entering it's hunting phase to attack you. Once the Ghost is in it's hunting phase the only thing you can do is hide. You should find the Ghosts room and place the Crucifix inside it and it will stop most of the Ghosts hunting phases.
Hey, you can keep on repeating the training over and over to help you understand what's going on. For the fingerprints, the Ghost will leave them on doors when it moves them as well as windows and light switches when it uses those. This can sometimes take a while so it's best to do this last.
The Ghost will stick to one room 90% of the time so it's usually best to use the EMF Reader first to work out what room the Ghost is in. Then setup cameras, ghost writing books and use the Spirit Box. Temperature can take time to drop so you can check this at the end.
Hope this helps. Let me know if you need help with anything else.