As I mentioned before I think your gf crossed a line in her job. But you must remember she cannot control anyone else and holding her responsible or questioning her about his behavior is rather pointless.

I do think that relationship will end badly (between her and client). I also think that she needs to establish some boundaries and quickly. My concern isn't so much for your relationship, it's for the client. They're very vulnerable. It worries me greatly. I would like you to try to step out of the relationship for a moment and consider him. He's not your rival, he is a very sick man. Your girlfriend sent him very conflicting messages by giving him personal information and accepting gifts.

My husband and I have been married almost as long as your girlfriend has been alive and if you listen to one piece of advice please listen to us on this. Throughout your future relationship there are things that are going to come up; you must express your thoughts honestly. Expecting your partner to know what you want deep down will only cause problems. I really hope that you iron this out.