The last two photos of Mystique are how I typically "collect" my Mustang at a trot. That looks normal for how I would ride a non-gaited horse.
I've been under the impression (however incorrect or correct), that with a gaited horse you want their nose out and you don't want to tuck them up and round their back. So I am trying to aim for something more like your first photo, or like this photo I found on Google:
I ride her with light contact, but not a totally slack rein. Similar to the guy in the photo above I suppose.
As for her conformation, I'm not really sure what she's built like, other than a broodmare, lol! She isn't the tall, lanky TWH type. And she is really wide in the chest, so I guess she is built more like a QH, but she really doesn't look like a QH either. Here is a good photo of my girl. I know it sounds silly, but to me she looks like a big Arabian.
What I really need to do is, get the neighbor down the road with Fox Trotter experience to watch me ride her and tell me what she is doing. Because I swear she hard trots when she gets going too fast. Or maybe it is a bouncy Fox Trot. But either way, it isn't her best gait. It really feels like a regular trot to me.
She does have a to-die-for flat walk. That is her best, most consistent gait. Friends horses will be trotting, and she will still be at a walk, lol! And when she gets excited she will do a running walk. It feels like her back end is gliding and her front end is a little more animated. I LOVE that gait but she only does it when she is really excited. So many gears, so little time!