Should you write down how the venue handles messages?
Yes, one sheet: who replies, how soon and what is not promised. A manual is unnecessary if only one person at the venue answers the phone and that is already clear.
Write to us. A quote with no commitment.

Note the message that sits unanswered on a Saturday. Each shift replies differently and the booking does not know if the table is held. You get that sheet by the phone, with the name of who covers the day off.