When you open Visual Studio 2015 and there is a pop windows to invite you to click on it for updating Xamarin and you click, nothing happends. There is a bug but clicking the update available popup was fixed in one of the recent releases. You can manually update in the Options menu under Tools.
As for the errors, I get those all the time. Support packages can often be a problem. Update to the latest XF package. Try deleting bin, obj, and the contents of packages folders and rebuild.