Xamarin provides access to the full platform API for whichever platform you run on. You can use Android's Camera2 API to automatically take photos from a Xamarin app on Android just as you can use UWP's MediaCapture to do so from a Xamarin app on Windows.
API doc: Android.Hardware.Camera2
Sample: Xamarin.Android - Camera2 Basic Sample. This isn't a Forms sample and is probably a bit out of date, but it should give some basic guidance on how the Camera2 API works.