I work in a Oncology office so things may be a little different.
-Walk ins- hate 'em, we have a triage nurse that can usually address most of the issues or triage them to schedule an appointment. You could appoint one person to deal with all walkins.
-Demographics are updated at every visit.
-Cell phone are a no no in patient care areas. I have gone to managers to talk to a coworker who is constantly on their cell. ( I personally don't get why people need to be on the phone all the time, you will see your family tinight hang up and do your job)
-we have 3 receptionists that rotate for breaks, so there is always someone at the desk. You could suggest having a sign that say" the receptionist is away, please have a seat and she will be right with you". If it is a constant thing I would talk to them or a manager.
-We try to get all walkins issues delt with while they are here, but sometimes there is no time and they are asked to schedule and come back.
I hope this helps,