Its hard to say exactly how close your feet should be, you really want to find whats most comfortable for you. But in your video, you don't look very comfortable.
Check out the top or finish of your reps. Notice how far your hands are away from your hips. Instead of hanging straight down, your arms are kinda hanging at an angle. Your grip is wide, so in effect, you have shortened your arms. This means you have to bend or stoop over more, and basically get into a weak/bad position. Its also way easier grip wise to hold the bar with your arms hanging straight down.
With your arms hanging straight bend over to the bar. The inside of your arms should scrape against the outside of your legs. Your feet should be close enough together that your legs don't force you to widen your grip.
Regarding the lower back/glutes; Look at the top of your second and 3rd reps. Your butt is still kind of stuck out behind you, like your legs aren't fully locked out, then you keep bending bending bending at the lower back. You want your back to be straight, like a lever or crowbar. The back is straight, while the hips push through. Instead of touching your lower back with the back of your hand, just smack your butt real quick before you lift to get yourself thinking about driving those hips through.
Again, its just a matter of feeling comfortable. Try a few different hand and foot widths. When you "get it" the deadlift should feel like a very natural, short pull. Almost like you cheated because the pull is so short and controlled.
Don't be bashful, post a link to your excellent "how I deadlift" explanation video. You really did a great job, and I'm basically just re-posting your material.