<p>doame has some great suggestions, and I think you have a good idea here, too:
In your case, your essay probably should be on this subject. Don’t make excuses, present what happened objectively and then show how you have changed, what you have learned, and what steps you have taken to be sure it doesn’t happen again (specifically the battery - the fake ID one isn’t as much of a concern). Or the essay could be about your personal struggle with the question of whether to reveal the arrests in your application.</p>
<p>It is definitely worth a shot. Best of luck, and come back and post how things go.</p>