Good evening Michael and welcome to the Events Calendar forum!
Thank you for your interest in our products.
We’ll be glad to answer your questions.
Can I add events in this same way? Is there an API that would allow me to add, edit and delete events?
Based on this specific set of needs, I believe your best bet is to use a third-party plugin such as wp all import (perhaps the Pro version depending on your needs): https://wordpress.org/plugins/wp-all-import/
I have personally used it on a few projects to create/update events.
Let me know if that helps.
Have a great day!
Geoff B.