Hi Willow_Creek,
Thanks for checking the plugin and I am glad you like it. 
Please find answers below.
Can you tell me if there is any way to add to and customize the status
choices beyond “Unanswered”, “Answered” and “Archived”?
Currently no, but this is on the immediate roadmap.
One thing you will like about the ticket statuses is that they automatically update based on replies. So an ‘answered’ ticket changes to ‘unanswered’ when customer sends a reply to a ticket.
Also is there any way to display a report of ALL the open tickets on
the front-end - even if a user didn’t submit it.?
At this point, on the front end, users (staff) can only see the tickets assigned to him and the ones that are favorited. Though you can see the detailed ticket reports in the backend.
Please feel free to post any more questions you might have. I will be happy to answer. 
Thanks.
Vivek