Mapsian enables you to easily create as many locations and maps as you want and manage them by groups.
You can create as many maps as you want. There is no limit how many.
No. You do not need a Google Places API plugin to use this plugin. But you can use if you want in general setting page.
Nope. Maps and locations are custom post type.
You can find the shortcode for each map and location on the Maps listing page.