Don't bring it up in personal statement! There's a place in the application that you can explain it. Also some supplementals let you explain any negatives of your application more in depth so that would be a good place for that
Not in your personal statement, but definitely bring it up somewhere in the AADSAS or, if nothing else, in your interview. I've heard of people being accepted, but dropped pre-matriculation due to a background check. Best to avoid that whole rollercoaster I'd think.
Hell No....that's interview material and even then if they don't bring it up, you don't even go near that....just to make you feel better, DUI is more common than you think among dental applicants.