I have also been struggling with this, it seems like the iPhone 6 (Plus) screens aren't implemented in Xamarin.Forms.
LaunchScreen
This is probably because Apple themselves are recommending the use of Storyboards and/or XIB files for your LaunchScreen as of iPhone 6, or better yet iOS 8.
I quote:
In iOS 8 and later, you can create a XIB or storyboard file instead of
a static launch image. When you create a launch file in Interface
Builder, you use size classes to define different layouts for
different display environments and you use Auto Layout to make minor
adjustments. Using size classes and Auto Layout means that you can
create a single launch file that looks good on all devices and display
environments.
This, in fact, is supported by Xamarin.Forms.
Just create a StoryBoard in your Resources file, configure your splash screen and select it as LaunchScreen in your info.plist file.

Advantage is that it works for all devices.
Background images
As for background images, according to the Xamarin iOS documentation this should work.
If it doesn't for Xamarin.Forms you should probably report a bug.
Meanwhile you could use a custom renderer like underneath, taken from the Xamarin Forums or check another suggestion from that thread:
[assembly: ExportRenderer(typeof(InfoPage), typeof(InfoPage_iOS))]
namespace Oxaco_BBC.iOS
{
public class InfoPage_iOS : PageRenderer
{
public override void ViewWillAppear(bool animated)
{
base.ViewWillAppear(false);
UIGraphics.BeginImageContext(this.View.Frame.Size);
UIImage i = UIImage.FromFile("Background.png");
i = i.Scale(this.View.Frame.Size);
this.View.BackgroundColor = UIColor.FromPatternImage(i);
}
}
}