I don't have much to add to what was previously said except this:
For spins, first make sure he can do a haunch turn on the ground. Much of reining should be taught showmanship style from the ground. Ie move should over, side pass, move hip over, back, move individual feet, etc. Once he can effectively haunch turn on the ground, you can begin mounted. Think of the horse this way: he is broken into three boxes. The first box is around his head, neck, and shoulder. The next is his belly, right under your leg. The last box is his hip and butt. For a spin, you need the last box to stay put while the front box moves over. Take your inside leg completely off of him, move your outside leg forward toward the girth (as if asking for a haunch turn), and bump his shoulder over with your leg and rein. Start slow and ask for one step at a time. Eventually, when you're sure he's moving the shoulder over, you can ask for more steps.
Also practice getting him to forehand turn and sidepass from the ground. Then you can translate to mounted the same way: forehand turn, tip his nose in a bit to the inside, and move your leg back to bump his hind end over. It's all about training to move away from pressure.
In regards to the correct lead, do one thing at a time. Your spins seemed frantic and disorganized, and the canter echoed that. Ask for the lope, and if he picks up the wrong lead, bring him back down and try again. Asking for the lope on a circle while exaggeratedly leaning into it may help encourage him to pick up the correct lead. Also having control over where his hips and shoulder are will help you be able to position him. To move correctly at a lope around a circle, technically his hip should be to the inside of the circle and his shoulder should be tracking on it, so that he is essentially (at least to start) moving diagonally around the circle. Watch some videos of pro reiners asking their horse to begin the lope from the middle (usually after a spin). You will see them pick their horse's shoulder up, move them so their inside front leg and outside hind leg are on the circle path, and then depart. Eventually the horse "straightens out" onto the circle as it has picked up the correct lead and is traveling along the curve.
Sorry to ramble. Hope that helps some :)
Great example of Shawn Flarida and Spooks Gotta Whiz. Skip to about 1:25 and watch how he moves his hip in to begin a right-lead circle.