i think you could benefit from dropping your stirrups down a hole or two they are quite high and is causing you to come out of the saddle quite a bit when posting. This will also help to keep you from tipping forward and give you a better seat.
I was going to suggest this also. And do some riding without stirrups. You look like you're perching and gripping with your knees rather than draping your lower leg around the horse.
Keep working on having a nice straight back and open front (like a sail filled by the breeze).
Agree with the other poster, your hands are better but still need to have thumbs on top. Think about holding ice cream cones in your hands--don't let the scoops fall off!
Think about having a straight line from the bit all the way to your elbows. Your elbows are locked right now. They need to give more with the horse's motion.
Lift your hands about 2 inches. They're practically sitting on his withers right now.
You pitch forward a little at the canter-trot transition (very common). As you improve your seat, you'll be able to "sit down" onto the horse's back to actually create that transition, and it will be a lot smoother.
Do you notice how much more consistent your contact was in this video than the previous one? And you were pushing your horse forward more, but he still needs to do more. There were several times when his head came behind the vertical and his hindquarters lost their push. With more flexible elbows and a more stable seat, you'll be able to handle that better and push him on into the bridle more. He looks like a nice horse and fun to ride.
My compliments on your willingness to take critique and your ability to put it to use! Keep working, I think you and he have a future together.