Wagtail
Horse servant
Absolute rubbish.
They can be used the same SJ as for XC. Sometimes the horse will not move quickly enough off the leg (through laziness, or distraction, or spookiness - for any reason) and will need a reminder coming in to a fence - the fences may not be fixed but coming into a decent sized jump with less than the right amount of energy or concentration can be dangerous.
Show jumped my mare up to Foxhunter level and had the ride on another mare too. Never once needed the whip. Maybe Foxhunter is not that big to you, but I personally don't really see it making that much difference through the grades. The most abuse of the whip I have seen in any sport is in showjumping.