I don't know about the reputation of the place you are at, but it isn't that bad from what I see . maybe not what you'd need as you got better.
I see improvement already. you are a quick learner and someone with a good natural balance. these videos will be precious to you in a year, when you will have forgotten how hard it was just to canter.
you are doing well and working yoiur way through all the things that have to be learned by time and practice.
as for a tip or two, learn early on not to look downward, or too far into your turn. your weight, and thus the horse's, tend to go where you are looking. Those times that the horse kind of circled really small, and leaning inward, YOU were leaning and looking inward. if you can develop the habit of looking upward, and a ways in front of you early in your riding, you'll never have to deal with unlearning the bad habit of looking down.