There are lots of drills to improve footwork. Cone drills, line drills, ladder drills, jumping, hopping, sprinting, etc.
Split step gets you ready for the next hit. If you do it properly, it unweights you meaning you take a short hop up. When you land, your center of gravity is in the middle so you can move in any direction quickly- left, right, forward, backward, etc. For example, if you are pulled wide to your forehand (assume righty) and you are running to your left back to the middle, your opponent can hit behind you and you won't be able to stop and switch directions in time. Lastly, split step allow you to react quicker and push off quickly in any direction, faster than if you were just standing there. Again, best way to describe this is return of serve. If you've been standing there waiting for a while, you will start to feel like a lead weight and heavy and you won't want to move to get the ball.
Make sure your fitness is good. It's ok to take breaks if you notice you're making mistakes (at least during practice). I was watching the women practice at the Bank of the West tournament today, and they were all taking breaks after 5 or 10 minutes. These gals are pros and supposed to be in good shape, and even they take breaks. I take breaks when I notice I'm getting tired or start making too many mistakes. After a minute or 2 break, I notice I move better and I have more energy.
Think of it this way. The key to a good serve is a good ball toss. Once I have that, the rest comes easily. For groundstrokes, you can say something similar. If you have good footwork, then I find the rest should be a lot easier.
