Don't ask your players to roll the dice unless failure has a consequence.

This mantra isn't particularly obvious in the rules of D&D as many times the checks are relatively pointless and failure at those checks doesn't really come with much cost. Failure is an opportunity both for you as the DM and for your players. Here are some ideas as to how to make failure have a cost in the situation you describe:

• A second attempt at picking the lock costs time, and the life of a hostage.
• The lock is ruined and the door must be forced causing noise and alerting the guards inside.
• This door is not an option and you have to find another way into the building.

These are three ideas of things you can have in mind if the check fails. The important thing is that failure should cost something (not a lot, it's 1 d20 roll, but something). Make it something small, the next encounter is slightly harder, the opportunity for surprise is lost, a later plot consequence etc.

Nothing major should depend on your character succeeding a skill check. This is because skill checks fall afoul of the Goblin Dice concept, which is that important things should not be decided by a single swingy die roll.

Don't let failure stall the action. Use it as an opportunity to move it forward, make it more interesting and to raise the stakes.

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.