I don't have anything to add to the jump critiques...
Your equitation pic, you seem stiff, and bracey against your horse; who is in turn bracing and behind the bit...he's also lost a bit of his drive from behind, because he is leaning on the front end. Relax a bit and let him have a tad more rein and I think you will look even better. You do look like a really cute team.
In the 'showmanship' pic, have him stand a tad bit further foward on his front feet, not much, but he should stand squarely under himself, not behind, or infront. His rear legs, for an Arab are perfect; one should be square under, and the other slightly to the rear. To help capture his attention, you are usually allowed to use a dressage or shorter longe line to 'cue' him...that way you can wiggle it higher, and enable him to stretch his neck higher. With Arabians, showing is all about showing off how 'alive' they are, and showing off the refinement especially in their head and neck.
"The ideal horseman has the courage of a lion, the patience of a saint, and the hands of a woman..."