I assume you mean open shows? Not gaited shows?
1. Yes, showing in a dressage saddle should be fine- quite frankly at our open shows the judges don't really care, as they've little gaited experience.
2. In a gaited class, you wear clothes similar to saddleseat- black pants, paddock boots, not field boots, not breeches. You wear a vest under a long coat and a derby, not a helmet- though, of course, if you are uncomfortable with riding without a helmet, you could certainly do so, as its not strict rule.
3. Judges will look for a controlled, nice looking horse. Balanced and power driven from the hind- the same as any other horse. However... how natural and relaxed both rider and horse appear will also contribute to how well you place.
Of course, this is all from a huntseat rider who shows & rides with gaited riders at open shows, so I guarantee someone else will have more to add or correct. :)