Well it sounds like your trainer pretty much told you what you need to work on. One thing that might help you is to ride with your thumbs on top, not your knuckles. Your wrist is breaking the contact with your horse’s mouth. You have a good rhythm and good legs
Your stirrups are a little short but if you feel comfortable with that length don’t worry about changing them. Do you ride in the pleasure division? If so, you do want to have loose reins (although not that loopy) and your horses neck long and flat and head tucked in. Make sure one rein isn't longer than the other. If you are doing regular equitation or hunters you will need some more contact with the reins.
ETA: The way you are arching your back is very, very, common among h/j riders. It's a trend that I wish would go away and a very hard habbit to break (I know I still do it
So in order to sit up straight you should feel like you are leaning back too far (at first) and then you will eventually feel more comfortable.