Welcome to the forum!!
The thing that strikes me the most from your photos is that your (super cute) horse isn't really truly working through himself. He isn't tracking up, and you can see that even though he's bringing his head down, he's still hollow through his back. The next thing I notice that even when his head is down, he's overbent, with his head behind the vertical - this is considered to be quite undesirable.
What I would suggest:
Drop the draw reins. They can force a horse into a headset, but that is far from being correct. Next, I would suggest completely forgetting about worrying about the headset for a while - concentrate instead on really feeling the horse start to drive with his hind end, and get a correct, even tempo. I like to call this trying to "feel the swing" - by this, I mean you want your horse to feel like it has "rear wheel" drive, and they're swinging their legs through a good range of motion, and tracking up. Play with transitions within and between gaits as well.
While you're working on impulsion, you want to be working on suppleness and straightness. By this I mean you want to be able to work the horse completely straight, but also ask for bend left and right as well. A couple of exercises I suggest for working on that are: serpentines (remember to get a few straight strides in the middle of each loop), 20-m to 10-m then back out spirals.
Through this, you should actually start seeing your horse round through his back, and come into a frame naturally. But, that is another post - I would suggest working on the above first.
I strongly suggest a trainer - they can correct minute things right then and there in real-time, rather than having it explained to you over the internet.
Good luck :)