Problem 1: It sounds like he is pretty stiff and is having trouble maintaining a bend. How is he when you're riding circles? Does he do the same thing?
Problem 2: My horse used to do this too. He definitely has a favorite side to travel, mostly because it's easier for him to stay balanced. It also sounds as though he doesn't have enough impulsion from his hind end (hence the desire to trot faster and faster instead of canter).
Problem 3: How big are your lunge circles? I started my horse on the lunge to teach him to canter as well, until I quickly figured out that he simply needed to build some balance and confidence before he could lunge a circle with correct bend, without popping his shoulders in or out, or transitioning downward from a canter to a trot or a trot to a walk.
The solution might be as simple as bigger circles! But then again, I don't know how big your current lunge circles are or if he has some sort of back soreness caused by tack or a previous injury.
Just remember, if his previous owner didn't work with him very often, he's going to have balance issues. He's going to be unfit. Sometimes it's okay if things take a while to learn. Plus, if he's only six, he may never have been taught to carry himself correctly.