How to directly render Compositing ONLY - without 3D scene? Does anybody have a solution in form of script, some addon or some 'hack' how to render only composited image sequences and passes that you have loaded in Compositing Nodes?

Blender doesn't do that directly because blender firstly render 3D scene (even 3d scene is empty) and then shortly produce render image for current frame from Compositing Nodes...

As you know blender Compositing can be awesome, I want use it like Nuke, but this is barrier for fast using in sense of speed-up post-processing.
Are you sure it does really render the empty scene (maybe add some meshes and lights to test this)?

If you only have file output nodes and no composite output blender will show an empty render image when finished with the compositing since it got nothing to show from your node pipeline. So just add a composite node as output to your node setup like John Roper said ...