She'll message me and then just disappear

I wouldn’t say she’s playing games but I also wouldn’t say she’s as interested in u as u r in her… I would say don’t take the situation too serious and start catching smth. But if u want to make sure that she possibly wants smth from u then just meet for some coffee

He'll do better to regard her as nothing more or less than a prospect.

yeah I'm not tellin him to start smth with her but I also think he would feel better when he knows how she's feeling/thinking towards him.
I would say some coffee is good to clear up all the questions but I definitely would not recommend starting a relationship with her

They'll do better to go through a getting-to-know-each-other phase first.

yeah obviously

seems like she wants you to take the lead, and is never the first one to initiate conversation.

possible yeah

Which is technically not playing games but it’s annoying. These behaviours doesn’t stem from a very good place, imo.

It takes two to put in the effort, not just one.