Finding the lat-long of the corners in a Google Maps window

Use getBounds(). From the doc:

Returns the the visible rectangular region of the map view in geographical coordinates.

That function returns exactly what you want: the southwest and northeast corners of your map. The first pair of coordinates are the lower left (southwest) coordinates and the second pair is the upper right (northeast) coordinates.

In Android(Kotlin) you can try this,

val curentScreen: LatLngBounds =  mapview.getProjection().getVisibleRegion().latLngBounds

var northeast=curentScreen.northeast
var southwest=curentScreen.southwest
var center=curentScreen.center
Log.v("northeast LatLng","-:"+northeast)
Log.v("southwest LatLng","-:"+southwest)
Log.v("center LatLng","-:"+center)