There absolutely shouldn't be an audience, I couldn't agree more with that part.
As for limited time, I think they should have more time to answer the questions. They should also be able to challenge each other and go back and forth freely, like the debates on Youtube. But also like the good debates, the moderator should make sure there aren't too many interruptions. Like, say one of the candidates has severe brain damage and can't stop interrupting Biden. Sure, his mic should be cut. But other than that, the moderator should allow for more free discussion, as long as they stay on topic.
Since its supposed to be a debate, those rules should be fine..Of course, Debate American Style. Means the full PT Barnum. That would suit Trump much better. But of course, no mouth breathing knuckle draggers or Roseanne Barr wannabes in the audience yelling will mean people will notice him not finishing a sentence..😷