I am actually quite sure that the clips are in fact in chronological order, although they do seem to have been edited. I'm guessing that the final tutorial we get to play will be somewhat longer than what we are shown here. And standing by my theory is not the same as claiming to be correct. As for me not answering all of your points, it was a bit of an onslaught. But in all fairness, I will perhaps answer one of them. In no. 6, you said:
Watching this segment of the video, we can see 3 males and 1 female above the vault. The female seems to be wearing a green dress, which matches up with one of the people we see above the vault in the trailer, as well as one of the skeletons we see in this area when we leave the vault. Also, if you pause the video and look at her feet, you can see that someone is actually standing behind her. Note as well the length of her hair, which seems to continue down past her shoulders. Now look at the very next scene. The woman we see here has short bobbed hair and is wearing completely different clothing, suggesting that there were most definitely 5 civilians waiting above the vault when we arrive. In addition to this, when we see our spouse and child from the protagonist's first person view, you can actually see the sleeve of the woman's green dress to your right, and the slightly balding chap with the checked shirt can no longer be seen, because he is standing to the left and is slightly out of the frame. Again this can be confirmed by comparing the exact same scene in the trailer.
As for the scientist, we know that he gets into the vault, and we also know he has a Pip-Boy, because we see our protagonist take it from his corpse as he leaves. If we go back to the trailer, in this exact same area (again, just before the blast) we see a vault security guard, a soldier in power armor and a scientist holding a clip-board. Even though the scientist is not wearing the Pip-Boy in this scene, it is most likely in one of the many nearby containers. He would then collect his Pip-Boy and put it on immediately before retrieving the huge red valve that has been placed on the elevator controls next to the silver lever that we see in this shot. This would have also been around the same time the bomb detonates. In the preceding shot with the dog above the vault during post-war, we can clearly see this valve above the vault, which I believe has been used to depressurize the elevator-shaft as suggested in my detailed theory post.
As I have quite clearly demonstrated here, there is a ton of information in the trailer and the E3 footage if you are patient enough to look for it. I have studied both of these, as well as other available material, literally frame by frame. And therefore my method for coming up with all of my 'theories' is actual rather scientific.