I need a way to do c# calls to save some data (coming from js function in a webview) in my sqLite.
Thanks in advance!
My guess is that this won't be directly possible in Xamarin.Forms. You will probably need to write a custom renderer for each platform. Here is an article on custom renderers: https://learn.microsoft.com/en-us/xamarin/xamarin-forms/app-fundamentals/custom-renderer/. You will probably need to write one for the WebView class. Once you've done so, you'll be able to get at the native control and use its underlying functionality. I recommend trying the UWP one first as that will be the most straight forward.
This article explains how to intercept a JavaScript alert in UWP https://code.msdn.microsoft.com/windowsapps/How-to-intercept-854d33da
But, you will also need to give more detail about what you actually want to do. What data do you want to pass back?