Just want to clarify, while the type of show might be called a hunter/jumper show, the actual discipline (or judge) is either "hunters" OR "jumpers". I think you already know this since you clarified hunters in your post
but I just wanted to get it out there.
1) The ultimate goal is to have the smoothest trip and to do that your horse needs to be on the correct lead. Ideally it'd be great if your horse would just land on the correct one! But if not, a flying change is necessary. The absolute worst thing you can do is break into a trot to change the lead (score drops to an automatic 50, and that's if everything else is perfect). Next worst would be to only swap in the front and go around on a cross canter. If your horse doesn't have a flying change, it is better to let them go around on the wrong lead, preferably as balanced as possible. Then to do either of those 2 things. Oh wait, I just reread your post. :) Training wise, you want to tell your horse when to swap, not let him anticipate. This needs to be done before the corner. Going around the corner on the wrong lead is not pretty, even if it's fairly balanced. But if i'm in the show ring and my horse swaps on his own, I don't punish it.
2) An overly arched back is a form fault that is usually a sign of a stiffness or weakness (or both!). Slightly? Could be due to the riders conformation. Please don't do this.
you want a flat back. However, judging-wise in the hunters the rider's position doesn't matter, it's based soley on your horse. The equitation ring is where a rider's position matters a little more.
3) You want a more natural headset.