If the horse is balanced, round, and collected when you are going forward and when you are backing up, then that is a good step toward having him stop round and collected as well. A trick that helps him become more consistent about stopping on the hind end is to back him up a few steps immediately following the stop. What I like to do is ask for a few steps forward, then ask for the stop, back them up a few steps, then just hold them there for a second or 2, making sure that they stay round in the body and soft in my hands the entire time. Then, I let them out and ask for forward again, let them go a few strides, and ask for the stop again. Repeat this over and over starting at the walk and progressing up through the faster gaits as they become solid in the cues.
That will get them stopping hard and fast and, if they are already round and collected, will get them really stopping good on their hind end.
Also, here is a decent video on teaching a good stop. He does it differently than I do and I don't necessarily agree with everything he does, but you can see that he gets great results.
As for the riding with your legs on or off them. I ride with my legs off the horse but close to their sides. The only times my legs really com into play is when I am cuing for something. My horses don't stop from the release of my legs, they stop from the shift in my seat. I take a deep seat and, depending on the individual horse and how they stop, I may put my feet forward just a touch. On a well trained horse, just that shift should be enough of a cue to get the desired result.
But, each trainer will have their own little nuances of how they train and how they like to ride their own horses.