Your lower leg is not really an issue. In fact , the lower leg should move a little as the horse breathes and if you really look at it, the leg only moves a little as you put weight into it then sit down (no weight), weight in (stand) then sit. It didnt move forward/backward. THAT is a problem, but flexing out and back a little is not a problem , especaially since I did not see you actually putting your heel on rythmically. Over all your leg is good.
In fact, let me tell the good first:
You ride very lightly and sympathetically. YOu are not bumping around and you allowed the horse to move both forward/backward and side to side in his barrel as he moved laterally. YOur leg stayed on him like a "wet towel" and your vertical position of upper body was good and moved very littel (have more to say about that , tho). YOur hands were pretty steady and you had a feeling of calmness in the way you rode. The horse seems pretty relaxed except for his barging the reins and head tossing, but that seems like ingrained school horse behaviour. Your transition to trot and canter was pretty good.
Now , the bad;
Your seat , while not noisy, is not strong either. YOu do not have your horse "connected" to your hands and your core. The horse is not really on the aides. He is kind of drifting along and just seems to happen to be going the way you want him to, and even then when he turns he is totally drifting either out or in throught the shoulder and has very poor balance. He is really draggging his front feet (evidenced by the amount of dust he kickes up, especially his right front). He is not connected at any time to his outside rein. I think he transitioned up to the canter in part because you were facing the gate, and he WANTS to go there because that's the way out to rest. If you asked for canter going the other way, would it come so easily? When he dropped out of the canter, was that your's or his idea? You didn't have a strong enough core to keep yourself from falling forward, and that was partly due to a weak seat and partly due to HIM making the decision to stop there. If you were more actively RIDING him rather than passively going along with him, you could have felt he was about to break and you could have put a leg on and picked him up and moved him on.
IN general , you need to work on more contact, having an inside and an outside rein and putting your horse between your legs/seat and those reins. Get some energy out of him, so he'll start to pick kup his feet and this will help with his balance. I can see that he is stiff, but it doesn't seem to be a real physical issue, but rather a habit of putting out as little as he can get by with.
I look forward to seeing a newer video.