Re: Student presidents
Our team is divided into subteams (known as groups), each with its own group leader. We do have a team captain, who addresses the team on a weekly basis during build season, covering very general topics about what the team has been doing. But the more unique feature for our team is the fact that at each meeting during build season we have one group give a (somewhat) formal presentation about their work over the past week or so, keeping the communication gaps bridged and also doubling as Chairman's Award presenters' tryouts.
One of our staples is trying to keep the students fairly close to equal in responsibility. As hard as that is to do in a de facto manner, we are at least fairly close to such a system de jure. The team captain is a senior, and his most important job is really just being a representative for the team when one is needed.