Your tone feels almost robotic in a sense. I a personality coming through but it seems like one that isn't too exciting or lively, which I'm sure you actually are.
each week, I take a chapter quiz in Biology, and each week, I finish far before everyone else. Each week, I open my books to check my answers, each week I find some wrong- and each week, I turn in my quiz without having changed any of the answers.
I understand your stylistic choice here but it comes off too choppy. Just make it a smoother sentence.
First, because my personal convictions would push me to follow the Honor Code to its fullest extent, I would neither partake in any of the forbidden activities listed, nor condone them in others. Second, I believe that I could act as a positive influence on those around me at Davidson, assisting them in keeping themselves free of any violations that would result in expulsion.
You wrote these as what you can contribute to the school. But these seem like given things already. This is your chance to talk about your characteristics and passions and how you will bring them to the school. Talk about them!
However, there is more to Davidson than just an Honor Code. Davidson is an academically and socially engaged community, committed to thoughtful discourse and an abiding sense of inclusiveness.
You literally copied what the prompt said. Don't, it comes off too generic and bland. Maybe here you can mention some of the more specific things at Davidson that you feel you'll be a good match with.