Until you can get your bylaws put together you could put forth that you will operate by Robert's Rules of Order. That would probably cover a lot of the areas where you have concerns. I would say that you put this option up to a vote at the next meeting.
I hate to tell you this, but all of those folks talking "behind the scenes" need to step forward and demand to be heard and demand a proper election. I'm sure your current Prez will attempt to make the lives of any who speak up miserable, but if you all stick to your guns, this bully(that's right, he's a bully) will have to give in. I would guess that it's probably not going to be a pretty thing, but your school needs the change.
You can try to make him see that change is needed: When you bring up the topic of elections, nicely point out that Prez was kind enough to step forward 3 years ago when no one else would take the job and that he has dedicated 3 years to the group and deserves a break.
Help!!! We have no bylaws that we know of, so we're in the process of writing them up. However, many of us have no faith in our Prez as he's outstayed his welcome and his conduct has been questionable (spending money with no vote, no minutes for some meetings). Apparently, the past members ran things very lax, so that's played his way. Prez has been in office for three years, have gotten and stayed in by a combination of offering the first year when no one else would and then almost a self-appointment for the next two. He's also in the principal's pocket, so disagreeing with him is not an option unless you want negative fallout (let's be honest, it does happen).
Because of his conduct, a number of folks new to the group agree behind the scenes that it's time to conduct things more above-the-board. How do we demand a vote? How do we conduct one without bylaws? We have an open-meeting policy when it comes to voting - whoever's there gets a vote. Can we take nominations from the floor? Do we have to have a "secret" ballot, and who counts it? Concern is that he will fix it somehow, but, again, fear of fallout keeps many of us from trying to get rid of him now. It has been mentioned that we need an annual meeting in May. How do we make sure he schedules it?