Re: walking backwards
I have dogs who back up beautifully in heel position, and I mostly shape the backing behavior with a bit of luring at first if necessary. My chow, Khana, was praised by judges all through Rally Excellent - I was told numerous times that she was the best backing dog of all the excellent level dogs. The majority of dogs I've seen in competition don't back well at all and I don't really think it's that hard of a behavior to train.
I really focus on heel as a position and not just a movement throughout the training and that helps tremendously with the backing up, left pivots and stepping sideways. Because my dogs think of heel as "have my shoulder/neck next to Mom's left leg, facing forward", they make a big effort to stay in that heel position regardless of where I move. While I do actually teach them commands that mean "shift your rump back" for the pivots, and "back up" for the backing, it comes fairly naturally because they have a big desire to be in heel position already.
Before I teach my dogs to back in heel position, I teach them to pivot their hind ends. I do this because I want them to have an idea of moving the hind end independently of the front end. And I also teach them a "back up" command where they are in front of me, and I have them back away. At first I can just step toward them and as soon as they shift weight back, I mark the behavior and reward. Initially I don't even expect a step - just a shift so that they are leaning backwards with the weight more on the hind end. And then from there I build into a step back, and then more steps back. I sometimes use a touch stick to help them understand that they can back up without me moving toward them (they're first taught that touching the end of the stick gets a reward, and then I move the touch stick so it's over the dog's head and when they step back to touch it, I mark and reward).
Once they can pivot at least 270 degrees (with me turning in place and the dog backing around), and can back up straight in front of me, I start the backing in heel position. Depending on the dog, I may do as Historian mentioned and use a treat over the head of the dog (or the touch stick) to get the first step. I'm very careful not to swing my left shoulder back, because that's a cue for the dog to swing the rump behind me - but, if they start to swing the rump out, I can get them to bring it back in by pulling my shoulder back a bit and using the "get back" (my pivot command).
The dog gets rewarded for even the slightest movement backwards at first (sometimes just for shifting the weight back, which is the first indication). I think that most dogs learn to back crooked because people rush the training. Rewarding for each tiny increment is going to make the behavior solid and correct.
The reason I rarely use any sort of wall or table or chair to make the dog back up straight is because that becomes part of the scenario to the dog, and most of the dogs that I've seen trained that way end up not having the best back-up. We've tried it both ways in the classes I teach and the general consensus has been that the wall ends up taking longer because after you teach the back, you have to re-teach it without the wall. So now I never use those in classes and the dogs are learning great without having something to block them.
I remember back when I first started teaching my dogs to back up and pivot - way before rally become popular. We just got tired of the normal heeling and I wanted to do more. So we started trying all sorts of things. Khana has been so much fun, as she will now heel on both left and right and do pivots, backing up, etc. on both sides. I've never had a dog that was so flexible in heeling. It's fun!
Melanie and the gang in Alaska