hmmm, I don't mean to be harsh but you did ask for opinions and I think you're on the right track, there are just some little things you could do to really improve.
I'm assuming all these were done in the practice ring? Sure looks like it because you generally wouldn't have another horse in the ring while you're in your class

I'm not a jumper (not by any means but I have enough lessons under my belt, just enough to know what a H/J would want in a photograph) I really prefer Western Events but sometimes we have a few trail jumps so, I've picked up a few things over the years about what works.
I think if you're looking to improve paying attention to the background would drastically improve these shots. See how the knees blend with the pony in the background in shot #7? Hunter/Jumpers are all about about the knees! you want them at their tightest point in the bascule and you want them to be seen clearly. #4 comes closer but you still have the vehicles in the back. Pick a jump and line that won't have that in your view then send your friend over the jump and practice, practice practice. Since you ride, I'm sure you know the spot,. If you're shooting a show, scout out the area before they jump and get the cleanest shot you can. Clean knees are really important!
In #3, I'm not sure what the pony is doing but I'm assuming he's being naughty, I could be wrong though. To be honest the shot doesn't do much for me other than I'm trying to figure out if he's doing a flying change or bouncing in place? The arc of his body is wrong for a pretty lead change which is what is also making me think he's doing 'something' wrong. Either way it's confusing and my least fave of the bunch. If you were going for the dramatic 'naughty pony' shot, he'd have needed to be more animated

The REALLY naughty ones make for lively shots, lol, the ones giving a little protest just don't add enough flare

And if this was a change, well....This doesn't show it well. Not sure what I can tell you to improve it. I'm not all that great at catching them in the right moment either but then I haven't really gone out and practiced them either. Like with the gaits, I'd assume like with most that it would look better at the greatest point of collection OR extension.
#1 is also in an odd point of the gait, For English horses especially, I like to see them 'up'. On the hind foot in the canter, right as it's being placed down, and the knee pop in the trot. This takes practice. LOTS and lots of practice and is why most non-horse people have trouble being an equine photographer. It's timing with the horse's stride. I'm guessing learning this won't be your problem, just keep practicing. You've almost got it in #6 and it could be fixed up pretty nice but you've chopped off the bottom of the front hoof

#5 is ok too,again, I'd do something about the background and maybe crop it differently, personally I'd probably crop out the rider and just make it a head shot. like #6 you've cropped it in an odd place. The spur draws the eye but is way too close to the edge of the photo for my tastes.
#2 I'd have cropped it higher, to include the chain on the browband and remove the 'blank' space of the cheek. It will take the eye off of center and give it more interest
JMHO.