The 2 things that will make the biggest difference will be: Learning to ride off the front of your thigh and opening your hips.
The first issue to tackle is how you hang your leg for dressage. The correct way is to ride off the front of the thigh. Your don't grip on with it, it's the way the leg lays. You don't want to either pinch or pivot off your knee or ride off the back of your thigh which is usually caused by tension. A correctly placed thigh will turn your whole leg in and your toes will point forward because you are riding with your thigh turned inward. You may have to physically grab the back of your thigh and pull it away from the saddle to teach you leg to lay correct.
By opening your hips you allow the horse to move up underneath you and follow his back with your seat. At first this will simply be a quiet seat that does not influence, but you will have to put your butt in the saddle to learn this first part! You need to have about 90% of your weight settled and centered in the saddle and 10% in your ankles and stirrup. That includes when you are posting and when you are cantering. Later, you will learn how to influence the horse with your seat more.
Once you get those 2 things down, you can focus on riding with your upper body straight. When you to that, you can bring your elbows back allowing them to bend which will help you keep a softer contact with your horse's mouth.
I like this horse's frame for a training level test. Although he could be more round, that is not required at this level. He is fairly rhythmic. He could be more accepting of the bit.
He needs some work in the transitions. Often a horse new to dressage will need a bit more warning than an advanced horse. So instead of just stiffening and holding the reins tight and dropping him down a gait, prepare him better. Five strides before the transition close your hand on the outside rein to say hey are you paying attention? Three strides away sit a smidge deeper in your seat and squeeze the outside rein saying ok are you ready? And then deepen your seat, close your thigh, and close your hand on the outside rein. The same goes for upward transitions, although he seems to be having an easier time going up than down.
For now, you should ditch the spurs. Your horse is being inadvertently punished especially in the canter. You don't want him to sour or become dull to the spurs. Carry a whip instead. It's better to ask for forward with a whip and use spurs for lateral aids. You can still work on bending and leg yields with a whip and you will focus more on your leg and gain proper strength in your legs provided you hang 'em right.
On other's comments:
Gloves. Yes! Always.
Heels. You should probably hike your stirrups up a hole or maybe 2 to allow your leg some wiggle room while you get your position sorted out. You don't need to jam them down like in h/j, but you should have some give and "bounce" in your ankles.
Hands. I don't mind them being low, but you need to have a bit more bend in your elbow and relaxed forearms to keep a straight line to the horse's mouth.
Posting too high. Let the horse do the work for you. Again, 10% of your weight in the stirrups. If you need to get your horse more forward, aid with your calves on the down or tap with the whip.