I have no problem with someone taking notes.
Make sure you have eye contact but if you write a few things down, it’s not an issue. Most of these interviews are really discussions. I’d certainly have the first couple questions I plan to ask in my mind - but that may change as the flow of the discussion may got.
You can check your schools website - often these interviews are informative, not evaluative - so don’t feel pressure.
It’s a conversation, but it’s your chance to learn more about the school and show how you might fit.
If notetaking helps you, as long as you’ve got solid eye contact as you answer, etc, I think it’s fine.
As for buying a drink, I’m guessing 9 times out of 10 the interviewer will buy you the drink. I wouldn’t offer. If he asks what you’d like, feel free to order. If he doesn’t, order and pay for yourself.
Thank them for their purchase (assuming they do) and thank them for their time. Then follow up with a thank you email - you can read on line how to write that.
Good luck.