To those of you who find you are sculling when you are distracted . . . As my Fundamentals instructor told me, sculling (unless it has simply become an ingrained habit) is almost always a sign of instability. If you use the fact that you are sculling as INFORMATION, you can figure out what the issue is that you are trying to correct with your hands -- correct it another way, and the hand movements will go away.
Often, sculling is an attempt to avoid rolling onto one's side. If one's BC doesn't fit well, isn't tightened down sufficiently, and lacks a plastic plate component to stabilize the tank, the tank can often be out of position to one side or the other, creating a definite tendency to turn turtle. This is pretty easy to manage with your fins, if your fins are stiff enough to take a good "bite" out of the water, but in my observation of OW students, it's difficult to learn to control this roll with split fins. Also, to stabilize oneself with fins requires that the fins be separated a bit -- if you tend to keep your feet together, it will be harder to do.
Sculling can also be an attempt to fight either being light or being negative, and again, if you're trying to push DOWN, you're fighting a tendency to sink; if you're trying to push UP, you're fighting a tendency to rise.
Hand swimming can be countered by either making a conscious effort to hold your hands together, or sometimes carrying a light will help, as having to keep the light on what you are looking at will effectively prevent wild hand motions
For the back kick: The best way to learn it is from someone who knows how it's done. But you can work on it yourself in a pool. Study the videos of back kicking that are on You Tube (5thD-X videos). The motion is an extension of the knees with the soles of the feet facing each other, followed by a "scooping" motion of the top of the feet out to the side. Get in a pool with a bathing suit, no fins. Play with this motion until you begin to feel yourself move backwards. (I've seen students get this in less than five minutes.) Then start swimming laps backwards until it's pretty effortless to produce the necessary motion.
Now get in the pool with fins (still on the surface) and do the same thing, until you can swim a full lap backwards without losing the motion.
Now put on scuba gear and go diving, and try it -- I think you'll be pleasantly surprised! (One caveat: back kicking is extremely trim-dependent. If you are feet up, you'll pull yourself back and UP (the shrimp dance). If you are feet down, you'll kick up silt and you won't go much of anywhere.)