This person isn’t a “friend”. A true friend wouldn’t think it was okay to manipulate and impose on others in this manner, nor would a true friend be imposing guilt on their host.
Many people are prayer warriors, including right on these forums. Praying is fine, but it does not give a person the right to camp out in your home, nor is that even necessary in order to pray for someone. If I pray for my friend Joe, I don’t assume it’s okay for me to crash indefinitely on Joe’s couch in return for my prayers or that it makes my prayers more efficacious to do that.
The priest probably wants you to try to be kind, but if you have to call the law then you have to call the law. I also can’t see the ending of this friendship as being a bad thing for you. This person needs help that you cannot give, and they seem to be pretty toxic. If I somehow ended up in this situation, I would first urge the person to leave on their own and if they weren’t agreeing, I would do whatever legally I needed to do to get them out.
One question - if this is your “apartment” that presumably you rent from some other landlord, are you even allowed to have somebody else who isn’t on the lease living there for 2 years? I would check the terms of your own lease to make sure you’re not in violation by having an additional roommate who isn’t on the lease. If you’re violating your own lease then the friend needs to go as of right now.