Hi,
Thanks for using our plugins and glad you like them besides those errors.
Unfortunately, the short answer to your question is AppointmentQuest does not interface at all with our plugin. I could not even guess at how their system works to help out on that.
The only option people have used as “Event Registration” is one of our ticketing plugins as it can create tickets per event. It is not a direct registration system though so it may not collect all the information you are looking for when someone registers.
I suggest going to the New User Primer for WooCommerce tickets:
https://theeventscalendar.com/knowledgebase/new-user-primer-woocommerce-tickets/
That will show you how the plugin works and if it might work for you. All the ticketing plugins have the same features so looking at one will get you an idea how the other 3 work too.
Let me know if you have any follow up questions.
Thanks