The full list lives in FAQ.
The calendar shows no available dates at all. Usually there is no price list row for that year, or none covering the current period. Check the Price List tab and the year picker.
The price does not multiply by the number of people. The product is in Guests (does not affect price) mode. To make the count affect the price, switch to Units — globally or on the product itself.
Why is 18–22 August five nights rather than four? The plugin counts every selected day, the last one included. The same rule drives both the price and the stay description.
A customer cannot cancel a reservation. Either the Cancellation cutoff (hours) window has passed, or the StayNotifications module is switched off.
Reminders never arrive. A daily cron job sends them, and on a site without traffic WP-Cron is never triggered. Also check that Enable reminder emails is on and that the store can send mail at all.