Hmmm. As usual, I guess I'm weird. For me (and my horses) there is walk, trot, canter (or lope) and gallop. In each of those motions, I expect them, within reason, to be ready to go faster or slower. For faster, I take a more forward seat. If need be, I'll whisper, "Pick it up" and gently squeeze. For slower, I settle back some. If that doesn't do it, then I use my pinkie - as the left shoulder goes forward, my left pinkie drags on the rein. Then right, left, etc. Usually they ease off within a few strides. I may add "Easy...", which always means slow it down a bit. "Eaasssyyyyy" means slow down more...
Practicing adjusting the pace is just like practicing a turn. In particular, my mare is easily bored...and when bored, she likes to liven things up. I'd rather she didn't, and adjusting her pace is a way to prevent 'boredom'.
I think of paces as gears. Just as I expect to be able to vary my speed in 2nd gear, I expect to do it at a trot. And just as I can redline my car in 2nd gear, I can trot a horse fast enough that a canter makes more sense.
As far as the stop-I often back them when I stop them,it keeps the stop sharp. Whether or not I am sliding my reiner....I want him to stop. It is actually harder to transition him to a slower (like a walk) gait, than to stop.