That's great! If she already backs up, you're well on your way.
As for leading and slowing down and speeding up--telegraph your moves to the horse, you'd be surprised at how much he watches you. Think of him out in the pasture--the lead horse makes him move with a look, the twitch of an ear, a lifted head, or the position of his feet. Your horse will watch you that closely, too.
Stand straight next to him. Click, say "walk on"--and lean forward just a hair before you start walking. If you want to speed up, lean forward a bit again, click, lift your feet higher, go faster in place for a step or two-then speed up--he'll follow. When you want to slow down, straighten up a bit before slowing down your feet. When you want to stop, stand straight up--as straight as you can (even lean back a hair), slow down in a step or two, then stop.
This really works--horses respond to the body language of other horses, and they will respond to your body language, too, if you pay attention to it and do it consistently. It's not just showmanship tricks or whatever for a horse show--it really, really works. You train a dog to heel the same way. Animals watch us--they watch our hands, our shoulders, our feet, our faces--they really do. That's how they communicate with each other, and that's how you can communicate with them.
Signal what you want a step or two before asking for it, and you two will be in sync in no time.