The touch and go method is really if your just using the box as a depth check. But that can defeat the purpose of deloading on the box which makes it much more difficult and thus effective (for what it does). The trick is not to relax and colapse your posture when you sit down. Anuj was actually doing that a little before....so that the back tightness is lost and it rounds out and all the tension goes out of the lower back....
The main key of course is not to crash down onto the box! That's actually one of the advantages cuz it teaches you control and deceleration.
But I'll let Anuj speak on whether it hurts his back
On your deads I think once you find your proper position behind the bar, drive through the heels and pull the bar straight up everything should fall into place...and it's not like it's terrible. You'll actually see people deadlifting in a similar fashion as a demonstration of good from. But in general (meaning your not going for a big max lift or record) your deads should be one fluid movement. Which is to say your BEST dead should be like that.
Let me put it in a very simple way. As SOON as you exert force on the bar it should move. There should be no part of your body that moves BEFORE the bar does.
It looks like your are maintaining your back when you sit down on the box better but I think you may be able to still keep it a bit tighter. Basically what you want to look for is that little backwards rock AFTER you sit down. You want to eliminate as much of that as possible and that will make liftoff much better and minimize any extra forward lean. But all in all it is really good.
Uni RDL's look really good too. I hope to see you getting some more flexibility and going lower on that kind of stuff in general. I'm behind on stuff and I know you still need the stretching program. I've just got some details to fill in.