There are a large number of valid answers:
a) Board Game: No. When you enter a pit square, you are immediately moved to the bottom and take appropriate damage. You can then continue your move from there.
b) Gamist: Yes. Conservation of momentum is going to make your head hurt. Ignore it. All momentum is lost.
c) Simulation (old school flavor): Partially. Normally, in D&D teleportation is assumed to move instantly through a space with no gravity - normally said to be the astral plane. When you teleport while falling, you subtract the distance teleported from the total distance of the fall. In the case of the example, the teleporter arrives at the bottom having fallen 5'.
d) Simulation (new school flavor): No. A fey step is non-instantaneous movement through a space which has gravity. That's why it requires a move action and not a free action. Hense, if you step out into this space while falling, you continue to fall, and when arrive back in the normal world you still have all the momentum you built up while falling in the feywilde.
For 4e, I believe that the 'correct' ruling is 'd'. A feystep isn't true teleportation. It's closest in old school terms to an ethereal jaunt, only the place you jaunt through is a much closer physical approximation of the real world than the ethereal plane is. However, do what suits your camapaign style.