When using Google Maps Android or iOS API, the map will show some place icons.
I want to know:
When using Google Maps Javascript API, there are also POI on the map. By default, you can click on them, and will show info window of the place. You can also disable the POI layer easily. However, I didn't find any relevant APIs to do that.

Google just added this feature in Google Maps Android SDK v9.6.
Now you can register GoogleMap.OnPoiClickListener to GoogleMap to handle onPoiClick(PointOfInterest poi)
It is stated in the Google Maps object documentation that not all icons on the map are clickable. For example, transit station icons can’t be clicked. However, markers that you add to the map are clickable, and the API has a listener callback interface for various marker interactions.
Now for your problem about Place ID, the Google Places API for Android has a documentation that can help you with it.
Place IDs are available for most locations, including businesses, landmarks, parks, and intersections. These IDs are stable, meaning that once you've identified the place ID for a place, you can reuse that value when you next look up that place. You can use the same place ID across the Google Places API and a number of Google Maps APIs. For more information about Place ID, just check the documentation link above.
I also suggest you to check this tutorial to know more about how android work with Google Places.
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