I am on my phone, so please forgive me if I answer a little wrong due to being unable to verify on Blender (let me know if you get Blender to compile on Android, k?)
The first thing to clear up is that the compositor works on single frames at a time, only. If you want to do basic Compositor-like stuff, you’ll have to use the layers and strips in the VSE.
Second, there is a checkbox in the Render tab, under post-processing, that has checkboxes to enable the Sequencer. If it is checked, AND the VSE has data in its timeline, then it is run instead of a Render when you [Ctrl+F12]. It will fall back to full animation render if either of those conditions are false.
So, this allows a good way to run things: 1) Render out to .png’s, 2) Add them as a strip in the VSE, 3) Set your output type to a video encoding. Now you can get a very quick video output by [Ctrl+F12], or you can in-check “Sequencer” and see your output back to .png and redo your full render with [Ctrl+F12].
One more thing: the VSE strips are only references to the images. If they change on disk (such as by getting deleted when /tmp is cleared on reboot, or if you render from another .blend), then there go your renders. This is why one of the first things I do when setting up an animation .blend is reset the output dir to something like //render .
Does this clear most of it up for you?