As mentioned and as the word indicates, “buddies” are associates/consultants early in their tenure and their job is to actually build a connection with you so that, if all goes well, they can sway you into signing for the firm they work for in the event of a cross offer. Their role is also to make you comfortable with the interviewing process and the firm culture. Therefore I would keep first email casual but polite, with a very brief introduction (they already know who you are and that you will reach out) and With the request of setting up a call to discuss the various questions you have.
for the call itself i would prepare as suggested in other replies by looking into background of buddy, preparing and organizing questions by topic, etc. Remember that call should be a conversation and not a mere Q&A, so try to find something in common (e.g. alma mater) you can converse about.
hope it helps,