Hi @Debbie / Terri,
Sorry for your experience that you and your potential guests are having. The verifications are setup to protect us hosts and the guests. I don't remember answering "personal questions", except for financial information, but maybe things have changed since I signed up for Airbnb.
The guest should have also understood your cancellation policy before booking and with ALL cancellation policies it states, "The Airbnb service fee is non-refundable."
https://www.airbnb.ca/home/cancellation_policies
It does NOT sound like they gave up as they were able to book your listing and then cancel so they must have been successful in setting up their account. I am also unsure what you mean by "selection procedure". As long as they can verify who they are and can pay for the booking, they can become Airbnb guests. I am also curious how Airbnb was "bothering them".
I do see how this has caused stress in the relationship between you and the guests but I would try to contact Airbnb and see if there is anything to do as they may waive their fee.
Please check out this How To guide in contacting Airbnb and I hope they can help you rectify the situation for the both of you and mend the relationship: https://community.airbnb.com/t5/Tips-Tricks/Contact-Airbnb-A-How-To-Guide/m-p/16165#M728
Good luck!
Dave
David
Superhost Ambassador ~ Host Club Community Leader ~ Community Expert ~ Experienced Co-Host