A Rectangle cannot support child objects. If you want a rectangular region that contains other objects, you can use a Canvas. You can also use a composite geometry, but in this case you would probably use RectangleGeometry rather than Rectangle. For details about how to create composite geometries, see Geometries.
The fill for a Rectangle or any other shape that has a fill area does not have to be a solid color. It can be any Brush, including ImageBrush or VideoBrush. For more information, see Brushes.