Well, I did some more research. I was able to get rid of the "quota" error message.
DPCalendar uses the Geocoding API. The instructions on the support website didn't exactly match the steps I needed, but you have to accomplish the same things:
Enable the Geocoding API for your calendar project (on the Google console)
Get a Server API key
Copy the Google API key and paste it in the Google API Key field of the DPCalendar Manager Options screen. That's where it gets a bit obscure: you have to open the Options screen, and then click on the Maps tab, to find that field.
On the event tab, there's a Map Zoom field. I found that 13 is a good number. A visitor can zoom in and out, it's just like any other Google map.
Unfortunately, I haven't been able to get rid of another error message. If an event has a location, the plugin will throw an error saying "another event from this calendar has the same alias".
I'm going to open a ticket for this.