Hello to Dutch Girl.
That is a lovely horse! Is he Andalusian? Lusitano? He has that look.
You are right, your legs are NOT right. Your weight cannot flow down into your stirrups because you are gripping with your thigh and knee. You can just see how your energy stops, right there. It makes you unstable and it looks like you are "riding" the reins a bit, except it's better in the second to last and last photo.
What's with the saddle? It looks like it's made out of plastic. Is it slippery? Can you try riding without stirrups for a bit?
Also, the stirrup is set too long. Your toe is angled downward as you 'fish" for your stirrup. If you relax your leg, let the weight drop down , down into your ankle, you will feel it flex a little and the stirrup length will feel better. Try shortening one or two holes.
Looks like you are having a lot of fun!