For your first question you’ll need to integrate to the google places API. See for example: https://javapapers.com/android/find-places-nearby-in-google-maps-using-google-places-apiandroid-app/
From there you can find the coordinates (lat/long) and display these on a (google) maps widget.
For question 2 I suggest creating a different post with more details on what you added and what you expect to happen. If the case is that the app store modules are not being displayed in Mendix Studio, then this is currently working as designed.