The audacity is amazing, however I guess it shouldn't be a surprise (although even I'm a tad surprised at this one).
With the audacity he showed with his cousin it should seem the "norm" but she is a blood relative.
Can he have a razor? Really. I would have immediately called 911 (or whatever your emergency number is) and asked them for help as your friend is suicidal.
Perhaps that is the way going forward with him? If he shows up again, just call the police. You didn't even hint there was an opening to continue any kind of friendship, you wouldn't even give him your phone number on his first visit, yet he showed up with his bags. He's probably not going to take no for an answer.
He'll be back.