How to get mouse position on screen in WPF?

You can use PointToScreen

Converts a Point that represents the current coordinate system of the Visual into a Point in screen coordinates.

Something like this:

private void MouseCordinateMethod(object sender, MouseEventArgs e)
{
    var relativePosition = e.GetPosition(this);
    var point= PointToScreen(relativePosition);
    _x.HorizontalOffset = point.X;
    _x.VerticalOffset = point.Y;
}

Do note that Mouse.GetPosition returns a Point, and PointToScreen converts the point to the screen coordinate

EDIT:

You can use the Mouse.Capture(SepcificControl);. From MSDN

Captures mouse input to the specified element.

I have little new found,

Code is below, fisrt build and run the Window ,

then just wheel your mouse one time on the window to invoke the endless screen detect of the Mouse Position.

(Thus I didn't find the way to detect mouse event out of the control in the second point of the question, but similar use an endless thread.)

But I just use a little skill to enable Windows.Forms in WPF Project, by simply use the Forms code in pure method, then refer that method in the Event Code Block.

.

Here's the Code:

Add two references to project:

System.Drawing 
System.Windows.Forms

Xaml part:

<Window x:Class="Test.MainWindow"
        xmlns="http://schemas.microsoft.com/winfx/2006/xaml/presentation"
        xmlns:x="http://schemas.microsoft.com/winfx/2006/xaml"
        xmlns:g="clr-namespace:Gma.UserActivityMonitor;assembly=Gma.UserActivityMonitor"
        Title="MainWindow" Height="350" Width="525" 
        MouseWheel="MainWindow_OnMouseWheel">
    <Grid>
       <TextBlock Name="TBK" /> 
    </Grid>
</Window>

Class Code:

public partial class MainWindow : Window
    {
        public MainWindow()
        {
            InitializeComponent();
        }

        public void KeepReportMousePos()
        {
            //Endless Report Mouse position
            Task.Factory.StartNew(() =>
            {
                while(true){
                    this.Dispatcher.Invoke(
                        DispatcherPriority.SystemIdle,
                        new Action(() =>
                        {
                            GetCursorPos();
                        }));
                }
            });
        }
        public void GetCursorPos()
        {
            //get the mouse position and show on the TextBlock
            System.Drawing.Point p = System.Windows.Forms.Cursor.Position;
            TBK.Text = p.X + " " + p.Y;
        }

        private void MainWindow_OnMouseWheel(object sender, MouseWheelEventArgs e)
        {
            //invoke mouse position detect when wheel the mouse
            KeepReportMousePos();
        }
    }

Why complicate things? Just pass null to get screen coordinates:

private void MouseCordinateMethod(object sender, MouseEventArgs e)
{
    var screenPos = e.GetPosition(null);
    // ...
}

Using MouseDown event of a control you can try this:

var point = e.GetPosition(this.YourControl);

EDIT: You can capture mouse event to a specific control using Mouse.Capture(YourControl); so it will capture the mouse events even if it is not on that control. Here is the link