Can I set up the single choices to be unselected once they have been selected?

 I see it is possible the user to unselect multiple choice questions but that is not an option for single choice ones. Is there a setting for that?

That is not possible with the regular fields.

However, you can use this widget and put limits on every option by 1. So whenever it is selected, it can't be selected again.

https://widgets.jotform.com/widget/gift_registry

Hope this helps!