Can a weapon with the "brace" special quality be used to gain the advantage against charges when:
A. User is mounted, Target is on foot?
B. User is mounted, Target is mounted?
There are no special requirements you must fulfill in order to be allowed to use the brace feature, nor do the mounted combat rules provide any particular restrictions regarding braced weapons. The action is the same whether or not somebody's on a horse, or underwater, or in mid-air, or any other situation in which the appropriate action can be taken.