You probably won't be asked about conduct violations. Just relax and don't bring it up since it will only hurt you.
Most questions secondaries ask are how you will bring diversity to their class or some variation of this question (I.e. how you are unique). They will also tend to ask why this medical school.
For examples, check out the class threads from this last cycle. The first post tend to include the essay prompts.
The only secondary that stands out to me in regards to reporting violations is Cincinnati. They even have you declare traffic violations, so I'd bet they'd have you include conduct violations. I can't remember any other secondary asking specifically about conduct violations, but it's been a year and a half since I've seen one so I've probably forgotten.
In certain states, traffic violations show up on background checks anyway. If you get accepted, most schools run a background check and depending on what your violation is, they may have some questions for you. If it's minor, it shouldn't be a huge deal.