Ok, a few things I see. Your saddle does look too far forward, if you look at that first picture, it definitely looks in the way of his shoulder. I'm not saying it doesn't fit, it may have just been too far forward when you were putting it on that day.
Your sitting up straight, I like that, but you're rounding your shoulders too much. Bringing them back square would probably lift your hands like everyone's talking about.
I love the last two trot pictures, those look great, he looks very forward and supple, very straight through the bridle and really nice. But the first trot picture, he's definitely not; picture two is not 'ifv good' in my opinion, it looks like he's leaning forward through your hands and lazy through the trot. If I had to guess, I'd say the canter work gave him energy and improved his trot vastly to what we see in the last pictures. I think that's the case with most horses starting out, and if that's true, then canter first! Do whatever you normally do at the walk, then jump right into canter work and get that energy up right from the start before you start schooling trot work. I know people are all about 'warming up slowly', but theres a line between warming up / allowing your horse to be lazy for the first 20 mins (what if you go to a show and only have 15mins of warm up? Your horse might just say, nah I have ten more minutes before I absolutely have to work). You can't say 'Ok Diddly, I know I said it was ok to trot badly earlier, but now its different'. So make his trot like those last pictures all the time!
Ok, the canter looks forward, that's a good step. But, it looks like he's racing around and not bending that hind end for collection. The first step is forward, and I think you have that, so now its your job to get him to sit down and take more of that weight on the hind end WITHOUT losing that energy level. Its a delicate balance, you need that jump through the canter, keep that, but really sit up straight and make him collect it back. I'm sure your trainer can help with that feel. The second canter picture, he looks unbalanced again, but also looks counter bent or at least twisting through the neck. Transitions through the canter (collect, extend, collect, extend ) and canter shoulder in are great for building strength to sit at the canter. Its hard work, so take it slow.
He really looks so much better though, make him look like those last pictures all the time!