The horse usually tries to compensate for the lack of strength in his back and haunches by seeking support in the rider's hands. So if your horse does this, you might want to consider adding some strength training to your horse's regime.
The sign of a good rider is that their aids are so subtle and smooth that you can hardly see what they are doing.
When working with a horse that does not have a great natural lengthening, make sure that you don't ask for too much too soon. Compare this to a singer who is training their vocal cords… they gradually expand their vocal range until they hit their limit. This helps
A good halt is square because it was a good halt. Not because the rider has taught it the "trick" of squaring up after an unbalanced halt.
If your horse finds lateral exercises more difficult in one direction vs the other (as many do), then they are not truly straight, or evenly laterally supple.