OK, I'll try to give you some advice, but it might be long though, lol.

I'll start off with the biting. You say he bit you before you mounted. The problem could lie there. Perhaps in his past, he has had experience of rough handling when being mounted, and he is reacting instinctively when he believes pain is about to be caused to him. You say you 'grabbed' a whip, perhaps this movement just shocked him. I would always approach him very quietly, and move slowly around him. Before you mount, take hold of the reins just below his mouth, where he can't bite you, but allow him movement in his head rather than a rigid hold. With your other hand, gently rub his neck and ears if he allows you to touch them. This will have a calming effect on him and will reassure him that you are not here to cause pain to him. Perhaps also check that he has a correctly fitting bit, biting and snatching at the reins can be signs that he is finding it uncomforable in his mouth.

The trot next. I know exactly what you mean about inconsistant trots being annoying. But, in the long run, it will make you a much better rider, and you will thank Casper for it.

Ok, evidently, kicking him doesn't have an effect. What you must never do whilst riding is to be constantly kicking with no effect, as this teaches bad manners. After three kicks, with no reponse, that's the time to use the whip. He needs a firm slap behind the girth (never on the hindquarters) to show him that you are confident and in charge. If he messes you about, you do it again. Now as you say he shot off, he responds to this, but not leg. This, to me, seems like a balance problem, as he's not prepared to respond to equal pressure on his sides, but a sharp touch on one side sets him going.

What you need to do is get a firm contact with him. Get your reins short, and I mean short. He'll fight you, but if he messes you around, he needs a sharp dig in the ribs, and use your voice too, this is surprisingly effective with horses. Once you're satisfiesd that they're short, sit back on your seat bones, take a good feel down the reins, and then gently squeeze with your heels. First time, you'll probably have no effect. But what you are trying to do is get him on the bit. This is the secret to good paces. When a horse is on the bit, they accept the rider's contact, balance more easily, and collect themselves in their back and strides. This offers a rider a more consistent pace, which feels like it's going somewhere without being tense, as if the horse is going to spook any minute.

Some horses are more natural at working on the bit than others, but it is possible with nearly all horses. I often ride a mare who has an overdeveloped neck muscle on one side, so she has terrible balance issues. Getting her on the bit is very hard work and can be very tedious at times. You'll probably find this too. Whatever you do though, don't be tempted to just keep shortening, as then he'll just pull you back, and he's going to win if that happens. What often helps is 10m circle work. Do you exercise in a 60x20m school? If so, try riding 10m circles at H, then M, then B, then F, and keep going all the way around. Be as picky as you can. If you weren't happy with even the tiniest aspect of the circle (eg he slowed on the turn, or it was a bit square) then do it again straight away until it's right. A horse has to listen to his rider when he turns on such tight circles or he'll be in a mess. The more you do this, the quicker you'll find he responds to you. If you're feeling bold, tie your reins in a knot, hold onto the pommel and do the same exercise purely with your legs. It'll help you to not rely on your reins and him to listen for your leg aids.

If you're ever doing any work in the school, and you see him drop his head and arch his neck a little, even if it's just for a second, give him a good pat and make a fuss of him! He'll soon learn that it's in fact far easier for him to accept your contact and free up his neck and back a little.

Right, onto the canter. Now I know this sounds weird, but uncomfy canters are better to sit to! The bouncier a canter, the more you feel the rhythm, and it will show you how to sit with the horse. I think the problem with his canter could lie in his trot. A bad trot makes a bad canter. Once you have achieved more collection and impulsion in the trot, you'll find the canter transition much easier, and he should fall into a better rhythm with his hindquarters powering him, rather than his forelegs dragging him.

He could also have bad balance, much like the mare I often ride. She finds it hard to keep on the correct canter lead, and often does flying changes ofher own accord whilst going around corners. This can be corrected with the rider's help. Do you know which one of your legs is stronger? Every rider, even if they don't know it, has a stronger leg. Your horse knows it, though. Many of us will accidently put more weight down one leg, especially when cantering. Personally, my right leg is stronger (my dad's footballing leg, lol), so I often tend to lean inwards on the right rein. You need to make sure that you are sat up straight with weight equally spread about your body, and that your reins are the same length, too.

With the bucking, it's a good thing to have a buck in a canter transition! No, I'm not joking. I ride another mare who does the same thing. As soon as they buck, get your leg on and send them forward. I mean, they've just freed up their back end, so they will now have no problem offering you a forward canter. If they have enough energy to buck, then they have enough energy to get going! Use anything niggly such as bucking to your advantage, and you will get results.

And finally, I'll try to help on the jumping, even though I'm a dressage rider and don't jump too often. Lots of horses are 'rushers' and it sounds like Casper is one of them. They see the jump and forget to listen to the rider and just go for it. This can be rather dangerous, as if the jump was large, and solid, it could result in the horse falling. This needs to be sorted out.

I would practice riding him in walk towards a small crosspole. He will try to speed up as he sees the jump, but keep doing the collection exercises I mentioned earlier to keep him listening to you. Halt him in front of the jump, as close as you can get. If he fights, turn him away and do it again until he stands still. You can then move it up a gear to approaching in trot and turning away (if you don't fancy a trot-halt transition), and then in canter. Approach the fence from different sides randomly so you have to keep him guessing, and this way he learns that sometimes you may not want him to take over and do what he likes over a jump.

When you do ask him to jump it, don't bang your leg on. Keep the rhythm you've achieved, which should be easier now, as he won't be expecting to jump it. If you find he does speed up, try a half-halt, and point your soles towards the fence, resisting the forward movement with your seat. You should achieve a better jump, with more forward feel and him getting his hocks underneath him when he jumps.

Hopefully you should get him to use the correct number of strides before a fence. I presume that you can 'see a stride', something which I have never been particularly great at (which is probably why I turned to dressage, lol), and then you should have little problem. A good approach is key to a good jump.

I don't believe in stronger bits or constant nagging at horses to achieve a result. I think you must always work for a result rather than relying on a piece of equipment, and with a positive mental attitude, and quick wit, you can do so. Nagging does them no good, you've got to be there mentally, rather than physically, to say, 'Well, if you're not going to work with me, then we'll do what you want to, only I'm going to make it harder'. It's about being one step ahead. It's the humane way to teach horses obedience, rather than fitting them in gags and lashing them with whips. That's my outlook on it anyway. I've got far more results from a tough horse in a snaffle than I ever did an obedient one in a double.

Well, that took me a long time to type, so I hope it helps!