Hi,
Thanks for using our plugins. I can try to help you get started on this.
is it possible to apply different styling to events depending on the category or tag that the events have?
It is possible with some customization, which we can try to help you get started on, but cannot provide all the coding.
You can use the body class to add a unique class to the html:
https://codex.wordpress.org/Function_Reference/body_class
Then you can use that class to style those events differently.
That class could be the name of the Event Category as well.
Let me know if you have any follow up questions.
Thanks