Can you use composite nodes in blender video sequence editor?
As in, no 3d elements in your scene, working exclusively within the video editing screen layout?
I am currently using Blender 2.76 RC 3.
While you can't use composite nodes directly in VSE strips, you can setup the compositor with an image sequence or video file input without adding any elements from the 3d scene.
Then in the VSE you can add a scene strip which gets the composited render results, so you can mix in audio and use any VSE specific features. You can also setup multiple scenes with different composite nodes and join them all in the VSE.
No. However, there are modifiers and effects that can be added to the VSE such as glow and colour changes etc. that can be applied to strips in the sequencer.
Yes, and that is the way to go for unlimited video tweaking. Follow this tutorial to make Blender VSE with compositor and keyframe-based node editor, along with standards strip effects, realtime.
2.79 : https://youtu.be/chIdSAR_8NY
2.80 : https://youtu.be/g1ZkPSLqGnU