If he needs auditory stimulation during the workday, he should be the one wearing headphones and listening to nursery rhymes or whatever else he wants so only he can hear it.

You've only been in it 6 months. He's shown you who he really is and how he feels is an acceptable way to treat you. Drop him and run.

It's clear that he is flirting with her and making inappropriate comments. He doesn't sound like a friend, so why does she need to continue responding?

It sounds like your girlfriend doesn't do a good job at drawing boundaries. She can easily be direct that she has a boyfriend and his comments are inappropriate and she doesn't want to meet up with him in person or continue chatting.

First of all, you should straight up ask him how he's feeling about things if you've felt like the vibes are off.

Secondly, from an outsider perspective, I think you should temper your expectations a little bit more to keep your own feelings from getting hurt. This guy is relatively fresh off a breakup of a decade-long relationship and now he's dating someone ten years younger than him. It kinda reads like he's in a rebound situation at the moment. I would definitely proceed slowly while you're figuring out what you guys are doing.

I really can't tell if this is a troll or not.

A polite kiss goodbye on the lips to a family member is very normal in some families / cultures. There's no romantic intent in them at all and they are nothing like a kiss you'd give to a romantic partner.

If you're getting jealous about her kissing her own mother and father goodbye, you are the toxic one.