When giving the aid to canter, let your outside leg sink down and back as the last part of your canter aid. If you lift your leg up and back to use it (as so many incorrectly do), you will end up losing your seat to some degree, and may also end up sitting crooked.
Train your horse to understand that he should stay at whatever speed you put him in until told otherwise. Remember that every time you allow your horse to make a decision about his speed or energy level (or don't realize that he has done so), you are training him to make these decisions on his own.
"Make him proudly independent of you so that he understands his job so well you merely walk the course and then show him the way. Tell your horse what you want him to do, and then allow him to do it." ~ Jimmy Wofford
Don't "sort of" have a contact. Try to either ride with a connection, or ride with a loose rein. That "in between" area where there is sometimes a feel and sometimes not, is where horses learn to fear and/or evade the contact.
Don't let your horse lean on your leg in the ribcage area. Teach him to yield to that pressure. Swinging the quarters out in response to your leg is an evasion, and is a very different response than truly yielding and bending in the body.
"The word Dressage is used precisely because of its double connotation for taming and training. One cannot train any animal without having its full attention and focus on the trainer. Taming—focusing the horse’s attention— is difficult because he is genetically determined by instinct and is programmed for multitasking. The rider’s job is to gradually replace the horse’s instinctive behavior with one of utter focus on his rider. This enormous change in the horse’s behavior— disconnecting from his instincts and focusing instead on his rider—can be earned only by a rider deserving of the horse’s total trust." ~ Charles de Kunffy
When a horse collects, his shoulders will come up naturally as he engages and lowers his croup. Do NOT attempt to artificially raise the front end. That would be front to back riding, which is incorrect.
"You can't teach someone to ride cross-country in one field, or even with constant instruction. It has to become a natural thing, and the only way to achieve that is to get out and do it." ~ Bruce Davidson
Eventers need a saddle for cross country that allows them to move their center of gravity back for drop fences or anything on a downhill slope. Make sure your saddle has enough room for this to happen.
To be truly safe when jumping cross country, both horse and rider should learn to love that deep takeoff spot.
Please note that a "chip" is not the same as a deep spot. A chip is when the horse adds a stride unexpectedly, usually because the rider is going for a long spot or otherwise interfering with the horse's striding, and the horse is out of balance. And that's where the rotational falls happen. A deep spot in balance is the safest place to be.
For the cross country phase of Eventing, we need to be able to keep our horses balanced at the gallop while riding over rolling, undulating terrain. Yet it is becoming quite common these days for horses and riders to do most or even all of their jump training in a flat, perfectly manicured arena.
Make sure you do enough galloping and jumping training out on rolling hills if at all possible, to become adept at keeping your horse balanced at the gallop with the added challenge of varying terrain.
You can't make a horse relax. You have to HELP him relax. The mindset of helping rather than trying to make it happen makes a world of difference to the horse. This might sound like an obvious thing to say. But I see a lot of riders somewhat angrily trying to force their nervous and anxious horses to calm down and behave.
When preparing for a jump from a galloping position, one should always sink down into the heel before any touching of seat in the saddle, and only THEN should you take the mouth if necessary. Taking back on the reins first will almost always cause resistance.
"The basic techniques, or what they call basics, are more difficult than what comes later, this is the Trap of Dressage. Correct basics are more difficult than the piaffe and passage." ~ Conrad Schumacher