Assuming you are referring to the ClassiPress theme:
1. No, customers cannot delete their ads, but they can pause them for their user dashboard.
2. If an ad expires, the action depends on the settings you as admin have chosen. You can either chose to prune ads (i.e. they go back to draft status and are no longer visible on the site), or the ad remains on the site.
3. Ads are listed in the order in which they were posted.