Great words of wisdom from Tom Gullikson concerning strokes and movement (paraphrased): Some tension should exist below the waist, none should exist above it. The difference between pros and amateurs is that recreational players move to the hitting zone at the speed of the ball, while the pros get there ahead of the ball.
That really illustrates the concept of good footwork and yes, the split step when your opponent hits the ball is essential. When he (or she!) makes contact... BAMM, a starter's pistol should go off in your head and you should burst toward the hitting zone with a step and partial turn routinely. Fixate on developing this explosive movement, even during casual hits and eventually you'll be ahead on almost every stroke.
The slice backhand requires contact more out to your side than out in front. I use a continental grip and maintain the "L" between my arm and frame all the way through the stroke; the wrist doesn't release. The elbow stays straight and the swing comes from the step, torso turn and shoulder extension. LEAN FORWARD through the shot as if you are bumping a heavy door open with your shoulder--it's definately different from the two handed bh. Be careful not to swing it too high to low.
Good looking strokes! Try catching the ball-on-the-rise forehand with a flat stroke more at stomach level. Keep it in gear and go after the ball, mister. You're on your way!