Is there any API or hooks for using with Booking Calendar ?

1) Currently there is no full API for using Booking Calendar plugin with other plugins or services.
Some hooks exist, but they does not documented well, yet. We are in process of improving this with future updates of plugin.

2) But still plugin have some useful functions and hooks for such purpose.
Please check this file ../{Booking Calendar Folder}/core/wpbc-dev-api.php
Here you can find some useful functions and hooks.