The EditorTabcontrol (of type TabControl) has a SelectedItem property, you can use that to identify which editor is currently active. From there you can get it's content.
To add a close (x) button you need can set the TabItem's Header property to a StackPanel (a horizontal one) instead of a simple string, and add a string (the filename) and button (with the text X or an appropriate image) to the Stackpanel. Then handle the Click event for the button.