If I want to choose an Item from the "Compile using Android Version" Dropdown, the only item I can choose is "Use latest Platform".
I installed the following SDK packages:
Shouldn't the program give me other options?
It seems like Visual Studio doesn't recognize your Android SDK.
Check the path of your Android JDK, SDK, NDK under Tools > Options > Xamarin > Android Settings, and make sure you point them to their correct locations.