Hi Faye,
Thank you for your interest in our Events Calendar PRO plugin!
We don’t provide support for Acuity Scheduling and there’s no easy integration between Acuity Scheduling and Events Calendar PRO.
However, it would be possible to add a button linking to an external URL. To do that, you would have to customize the template for a single Event. We actually have a Theme’s guide which explains the process.
Regarding the mini-calendar in the sidebar, it would be similar: to replace the square date icons by images, you would have to modify the appropriate widget, still following the rules as explained in the Themer’s guide.
I hope this answers your question.
Cheers,
Jeremy