YOu are a very astute and honest observer of yourself and have the makings to be a dandy rider, especially with such a willing attitude toward receiveing a critique.
And, you look darn cute on that Fresian mare!
However, there is a very fundamental issue here that is part and parcel with the problems you mentioned, primarily your posting and your hands and your chair seat.
You are not aligned OVER your feet. Therefore, your weight and energy stop at your knee, which is pinned against your horse's side and from which your are levering yourself up for each of the posting rises. This means that you end up "flumping" back into the saddle with your butt pressing into the Cantle of the saddle. One can see it clearly being depressed with each flump of your butt into it, and the mare's swishing tail tells me she does not appreciate it. If I were to do that, at my 200 lbs, she would be very pissed off at me, but since you are slender, she can tolerate this.
However, it is a weak way to post and means that you are always BEHIND the motionn and depressing the horse's energy and encourabing it to hollow out its' back.
Look at how long your stirrups are, how far in front of your hip (the front of your boney pelvis , not the pubic bone but the big arches on each side) that your toe is. It should aobut line up with the front of your hip bone.
See how your lower leg and foot kind of flop around, but the rest of you is kind of stiff? That's becuase they are not working for you . Instead of levering up from a point (your knee) which is in front of you, you need to kind of be "expanding" and "contracting" throug your ankle, knee, hip in a line that is stacked over each other, like a jack in the box? You focus more on the down part of your post, too, so that you set yourself down in teh middle of the saddle instead of "bouncing" off the cantle.
Shorten your stirrups. Two notches. Take your leg out of the stirrup and lift them straigth out to the side, then let them fall naturally against the hrose's side. Reach down and put your hand on the outside of your big thigh muscles and pull them outward and upward, so that it kind of makes your knee rotate inward toward the saddle. Let let hang again. Lift your toes up and find your stirrup.
Now practice going up and down while the horse is just standing. You need to be able to post whether you are being bounced off the saddle or not, and it's more of an "unfolding" motion than a scissors pinch at the knee, from which you swing up and down.
Doing this will help your be able to stay more in one place in relation to the front to back length of the horse (when you lever off the knee , you are closer to the mouth, farther away, closer, farther away , which is hard to adjust to with your elbows to maintain a steady contact).
YOu have a nice vertical upper body and keep a good head up position. When you get this kind of posting that is over your own leg/foot you will feel a huge change in your riding .
Good luck and thank your for being so brave.