Following the instructions here: https://developer.xamarin.com/guides/android/getting_started/hello,android/hello,android_quickstart/
First, install Visual Studio or update it (via the VS installer) to include Android SDK, as described in the page that the tutorial links to.
If the .csproj files won't open, it's because you're missing some components - go reread the Visual Studio update instructions and check.
Update the Android version of VS at Tools>Android>Android SDK manager.
If it claims you're running the wrong version of Android (even though you've edited the properties file, and it's fine), open the .csproj file in a text editor and check.