So here is what I have now:
1) I deleted layer “Full comp”
2) I clicked “render animation” and first frame was good (approx 12MB) – as intended, and it looks like this:

3) but in following frames only 3D elements were rendered on black (non transparent) background and it looks like this – and obviously file size is down to 2MB:

4) This leads me to think, that maybe there is some issue with movie clip node? Looks like every next frame is not updating as it should…
5) and here is the weird part: if I select any next frame in timeline and hit F12, frame renders correct, but when “render animation is clicked, all these issues (mentioned above) are coming up…
no solution so far…