All the way down, completely flat on the shaft
For a short time the skin will remain bunched up a little bit away from the glans, but it will soon be bunched up behind the glans.
As for the other questions: are the video and the photo your penis? Because then I can say it looks like there's no tightness whatsoever since that foreskin goes back very far on the shaft. If it's not yours, well, it's not necessary for it to be able to do that, so don't worry! 
Not my photo/video. By the responses in this thread, it sounds like most are able to pull their foreskin all the way down the shaft, smoothing out the inner foreskin (just like in the video). I have no problems pulling my foreskin all the way down the shaft when completely soft. When hard I'm definitelynot able to do that, the farthest I can pull back is right behind the head. If I tug really tight, I can expose a bit of inner foreskin, maybe about 5mm/0.5cm - not even half the width of a pinky finger. As soon as I let go, most time it will stay behind the head but not always.
Like you said, it's not necessary, but I would like to be able to have my foreskin move more freely. I've flirted with the idea of having my frenulum cut, but don't trust myself enough to do it on my own. My only worry with a cut frenulum is that the foreskin would never stay behind my glans when erect because nothing would be there to 'stop' it from rolling forward.. I should probably see a urologist, lol.