Yes. This plugin is multisite compatible.
Yes. This plugin is compatible with all the themes.
You will need to configure API key inside plugin admin section.You can follow these steps in order to configure API key :
Create google API key from here, follow this article: https://developers.google.com/places/web-service/get-api-key
You have a tab inside your BuddyPress profile section named “Add Place”. There you can add your check-in place and date.
You can see a tab named “My Places” inside your BuddyPress profile section, where you can see all your check-in places list.