As far as I know, you are correct about your first question. After the first drawing (they look at all 5 of your hunt choices), any tags that are leftover will be available for a second drawing. You have to reapply though for those tags that are leftover. Everyone's name is not put back into the hat. The NV guys will know better than me but I can't imagine there are hardly any tags leftover. Maybe a few cow or doe tags but I can't imagine much more.