Hi @Donald369
I'm a highly experienced host and cohost and I too am struggling to understand what you are saying.
What is it your guest should be filling out? Why would your guests have to send your home owners association cheques? Have you made this a condition of booking on your listing/in your house rules that the guest needs to pay extra money directly to the HOA. If not you cannot enforce this.. Why are you assuming the guest is lying rather than post going missing or a mix up at the HOA?
No the guest won't necessarily get a notification from Airbnb that he has a message unless he signed up for receiving them. Many guests don't.
The guest will have paid when he made his booking;.
If you can give us an understanding of what the actual issues are we can try and help.
There is no reason to believe his reviews are fake.
You can of course cancel but you will be rightly charged cancellation penalties.
It seems that you would benefit from familiarising yourself more about how Airbnb works as a platform to market your STR business. The Airnbnb Help website is a good resource.