im sorry to hear you can only ride once a week, i sure hope that changes for you!
in the first jumping picture, your upper body is in a great place. yes, your leg has swung back a few inches, but its not bad. your heel is good, and i think you would benefit taking your foot out of the stirrups just a smidge more, it should be on the ball of your foot.
in the second picture you are only using one hand..not sure what happened there lol, and you are slightly too vertical with your upper body, unless this is a sitting trot. the "classical" position would be to have the same angle in your back as your calf angle.
in the third picture, your leg is right where it needs to be, relax your shoulders back some, and i like that you are looking up and that you dont lay on your horses neck. you should take up the slack in your reins, to have a soft contact with the mouth and your hands should be up underneath your face, at least. think of having your hands half way up the neck, and dont be afraid to grab some mane! it wont hurt your horse :)
in the fourth picture, your upper body angle is correct and your hands are in a pretty good spot with your thumbs up :) however, you want to ride without stirrups as though you still had them, so flex that ankle and get your heel down and legs wrapped around his/her? barrel.
in the fifth pic, the only thing i notice is that your hands are a little too low and your hands are a little flat. you want to ride as though you are holding two ice cream cones, and you dont want to ice cream to fall off! lol!
in the last picture it looks like you are trying to pick the pace up a little. once again, lift your hands up about 3 inches above and over the withers, its okay to bend your elbows, they are your shock absorbers. tilt your body a little farther forward to almost match your calf angle, and i can tell your are trying to squeeze her forward, but still try to maintain the depth in your heel.
overall, you look like a beginner, and only being able to ride once a week doesnt help that, but i think you do have some great potential. i envy your long-legged slenderness lol! if you go and look at the top equitation riders, they all have pretty much the same body type :)
as for your horse, she looks to be on the lazy side, but sweet and reliable at the same time. deffinately a good horse to learn on. (the lazyness makes you work harder ;D)
good luck, and i am glad you have a trainer that you like!