1) I agree the header could use some work. Having the facebook login below and your full tagline description in a fairly boring font and colors just doesn't to it for me. I'd work on this area, as it is a glaring issue with the design of your site.
2)You could make it responsive, but only to a certain point. Is 3 columns of videos too much? 4? 5? do some a/b testing and see if a certain column size results in more videos watched.
Also, where you have a single video per line, if you did make it responsive, would all the text end up on one line, and therefore leave empty space next to the video?
3) I completely disagree here. Whites pace is an important design element. I think you've used it well.
Now for my further comments.
1) the share buttons are awkward as you have them spread out across one long line. I'd keep them close together, and play with the positioning. You'd likely automatically assume that the left hand side is the best spot, but that may not be the case. I think the far-right, and offset from the video might work, or inline with the video player. I suspect the more these are squeezed together, the more impact they'll have. They just seem to be floating around disconnected from the content at this time.
2) I like how your top two items show how many videos are related to that story. It is a signal in some ways of the importance/popularity of that story. But why don't the other videos on the page have the same display? I'd like to see some consistency in that.