How do I display three months in the event calendar view?
It doesn't look like there isn't anything in the admin that will give you three months. I've implemented some similar solutions with custom calendars. 

There are a few ways that you could do this. I'm not going to get to far into the code, but just describe what I've done (I don't have a multiple-month example).

Method 1) Duplicate the monthly view and  alter the defaults in the contextual filter. Display these multiple blocks or feeds on a page.

Method 2) Create a custom node for displaying 3 months. Pass the contextual filter to the same view. Twig Tweak can handle passing arguments, though you may end up needing to do more preprocessing what Twig Tweak allows.