Honestly I was hoping for a more specific answer than “it’s impossible” or “you can find the answer somewhere on the internet.”
Even if the icons are determined by Google, you may be able to add or use them in your script (there are plugins for wp that is capable of displaying icons in google maps). Is not it?
In the following link I have not found useful information on how to display on the map the events of a single category.
I have a separate page that displays a map, but in contrast to other views (list, month) displays all events, not just those in the selected category.