The pony is cute, and has a lot of try in him.
I'm not delighted with the way this fence is built; unless your goal is to teach the horse to jump long and flat, building an oxer that's wider than it is tall is a bad idea, as most of time to goal is to teach the horse to jump up and round, using its back.
I am glad to see that you are using groundlines, and using them appropriately.
He also isn't engaging evenly (pushing off with both hind legs at the same time and same place) - all his jump is coming from pushing off with the right hind, because the left hind is back, which speaks to greenness.
If you brought me this pony to train, or brought him to lessons, I'd go back to cavaletti and crossrails until he understood how to bring both hind legs up under him and push off equally, and then work on little grids to get him snapping his front end and see if I could get him to bring his forearm to horizontal or above. I'd also take him out of the kimberwicke; there's just too much risk of popping him in the mouth accidently, and that's a whole lot of bit.
If I were coaching you, I would have you shorten stirrup a hole or two, and do some work in two point to solidify your lower leg, and then work on your hip folding an appropriate amount for the size of the fence. In these photos, your upper body is jumping a 4' fence while the pony jumps 2'. Getting your hand and arm out in front in a more appropriate crest release will help with this. When you plant or fix you hand by the withers, your shoulder and upper body try to follow the horse's motion and do the job that should be done by your hand and arm. Allowing you hand and arm to come forward will allow your upper body to stay up and back.
I try to stay out of helmet discussions, because I do believe it's a a personal choice, and that people have the right to make their own decisions, even bad ones. But I do have to say that I would never get on a greenie without a helmet, let alone pop over fences and I would never allow anyone in my barn to do so either.