No, it's not.
When lifting the other character you are either taking an action, or you interacting with an object -- depending on your DM's rulings.
If the DM rules that the pile driver is an attack (which I'd argue it is), that would cost you an action, and you can only repeat it if you have movement and an action to spend on it. This assumes you've grappled them, and have an attack left.
If the DM rules you are use an object. If it wasn't an enemy, you'd only be allowed to pick it up once. Once you drop it (which is free), it is no longer a free action to pick it up again. Use An Object action:
You normally interact with an object while doing something else, such
as when you draw a sword as part of an attack. When an object requires
your action for its use, you take the Use an Object action. This
action is also useful when you want to interact with more than one
object on your turn. (PHB 193)
Since you can't lift someone and do something else, it might take a full action to lift someone above your head. Remember that a round is 6 seconds, dropping someone more than once (or twice if you have the actions for it) would take about that long. Moreover, really can't lift someone and jump while doing something else, so it could be argued it can't be an interaction and must be a "Use Object" action.
To rule otherwise would allow a free 5d6 damage without using any action, and that, while awesome the first time (and a DM may allow it once, by Rule of Cool), is game breaking.
No.
You cannot take a 5-foot step upwards because doing so would take at least 10 feet of movement, which invalidates the 5-foot-step action and becomes a Move Action instead.
Anytime you cannot spend only 5-foot of your movement to enter a square, it should require a move action, and thus it is no longer a 5-foot step.
You can move 5 feet in any round when you don’t perform any other kind of movement. Taking this 5-foot step never provokes an attack of opportunity. You can’t take more than one 5-foot step in a round, and you can’t take a 5-foot step in the same round that you move any distance.
If you moved 10-foot, it is no longer a 5-foot step. This has been discussed on paizo's messageboards here and here.
According to James Jacobs (Pathfinder's Creative Director), a creature should not be able to fly upwards as a 5-foot step.
The only exception for this, back in 3.5, was creatures that had Perfect maneuvering, which allowed them to move upwards without using double their movement, so they could move 5 feet upwards without using 10 feet of their movement. This exception no longer exists in Pathfinder, but if a creature has a similar ability, the exception should apply.
Best Answer
Grappling (PHB, p. 195) states:
Movement and Position (PHB, p. 190) states:
(1) Therefore, if the steeder has a creature grappled, it won't be able to jump, unless the grappled creature is small or smaller. Alternatively, some effect might have increased the steeder's speed to 60+ without a grapple, and the halved speed is therefore still 30+.
Note that dashing doesn't help you here - it only increases your movement (PHB, p. 192), while your speed is still unchanged (e.g. at 15 feet).
(2) The steeder's leap is different from the regular jumping rules in the PHB, hence, all relevant rules can be found in the steeder's description. Since it can either expend all its movement to jump 90 feet or not at all, there is no halving of the jump distance.
Either it can jump 90 feet, or not at all (barring the regular jump rules, which of course still apply).
(3) Grappling also states:
Breaking up your move (PHB, p. 190) only mentions
Now, releasing a creature doesn't require an action, but I think the intent is clear - yes, you'd be able to release it during the jump. That also makes sense from a logical point of view, which is what I always try to take into consideration when I make any rulings as the DM.