How do I know if a WPF window is opened

You can check if m_myWindow==null and only then create and show window. When the window closes set the variable back to null.

    if (this.m_myWindow == null)
    {
           this.m_myWindow = new MyWindow();
           this.m_myWindow.Closed += (sender, args) => this.m_myWindow = null;           
           this.m_myWindow.Show();
    }

In WPF there is a collection of the open Windows in the Application class, you could make a helper method to check if the window is open.

Here is an example that will check if any Window of a certain Type or if a Window with a certain name is open, or both.

public static bool IsWindowOpen<T>(string name = "") where T : Window
{
    return string.IsNullOrEmpty(name)
       ? Application.Current.Windows.OfType<T>().Any()
       : Application.Current.Windows.OfType<T>().Any(w => w.Name.Equals(name));
}

Usage:

if (Helpers.IsWindowOpen<Window>("MyWindowName"))
{
   // MyWindowName is open
}

if (Helpers.IsWindowOpen<MyCustomWindowType>())
{
    // There is a MyCustomWindowType window open
}

if (Helpers.IsWindowOpen<MyCustomWindowType>("CustomWindowName"))
{
    // There is a MyCustomWindowType window named CustomWindowName open
}