Advice for dinner with prospective Ph. D. advisor and grad students?
To add to the Massimo's comment on not taking notes, yeah I think that would seem weird. If the conversation is about science, and a particularly interesting point comes up or you want to take note of someone's name to look up a paper, make a note on your phone.

Offering to pay might be polite, though if the prof's paying through his department or a grant I wouldn't insist. I think it's safe to say that if the grad students don't pull out their wallets, neither should you.

Just act normally. Be yourself - it is not a formal occasion. The prof will have invited his students along for two reasons:


Because dinner with just the two of you could be exceedingly awkward
So that everyone can get an impression of how you'll fit
in with the group.


Just make the usual small talk with his grad students to (hopefully) find some common ground, talk a bit about their projects, and make sure to have a good yarn about non-work-related things too. Your scientific prowess will not be assessed at the dinner table!