Can Bigby’s Hand move creatures that are Grappled into the air?

Bigby’s hand can grapple via Grasping Hand. This allows:

The hand attempts to grapple a Huge or smaller creature within 5 feet of it. You use the hand’s Strength score to resolve the grapple. If the target is Medium or smaller, you have advantage on the check. While the hand is grappling the target, you can use a bonus action to have the hand crush it. When you do so, the target takes bludgeoning damage equal to 2d6 + your spellcasting ability modifier.

With a strength of 26, can it move creatures? Not only do you get the action, but you can:

When you cast the spell and as a bonus action on your subsequent turns, you can move the hand up to 60 feet and then cause one of the following effects with it.

So, after a grapple, could I move it 60′ in the air? Then next turn move it another 60′ and cause the crushing damage? At some point while it’s way up in the air, release the grappled creature for falling damage?

What happens when you have a creature grappled and use the Bait and Switch to move 5 feet away from the creature?

Does it just break your grapple since the creature is outside your reach? Does this count as "Moving a Grappled Target" and the creature you’re grappling moves 5 feet with you?

Or does this count as the latter, but since your speed is halved, and the maneuver only allows you to move 5 feet, your speed is 2.5 feet, and if playing on a grid, actually cannot move?

Does improved grapple count in determinig the CMB when casting while grappled

I’ve always stayed away from grapple & overrun rules, but, this time, i can’t ignore it.

The rules says that

A grappled character who attempts to cast a spell or use a spell-like ability must make a concentration check (DC 10 + grappler’s CMB + spell level, see Concentration)

so does the feat, special abilities, objects granting bonus on the grapple check count against the DC of concentration?

Does the bonus like flanking count?

does Psi Warrior’s telekinetic movement allow you to move a grappled or restrained willing creature?

Telekinetic Movement. You can move an object or a creature with your mind. As an action, you target one loose object that is Large or smaller or one willing creature, other than yourself. If you can see the target and it is within 30 feet of you, you can move it up to 30 feet to an unoccupied space you can see. Alternatively, if it is a Tiny object, you can move it to or from your hand. Either way, you can move the target horizontally, vertically, or both. Once you take this action, you can’t do so again until you finish a short or long rest, unless you expend a Psionic Energy die to take it again.

It lacks any clause for the creature, just that they have to be willing

Does the Orc’s ‘Aggressive’ racial trait allow you to move with a grappled target as long as you move toward it?

Aggressive. As a bonus action, you can move up to your movement speed toward a hostile creature you can see or hear. You must end this move closer to the enemy than you started.

That last clause seems to indicate the negative, since a grappled creature would move with me even if I was moving toward it, and therefore not closer to the enemy than I started?

Does Improved Grab pull in the grappled regardless of weight?

Reviewing the choker I noticed the default strength is only 16. It caused me to wonder if an improved grab can pull a creature up in the air even if the strength does not have enough to carry (envision either a very heavy character or a magically strength reduced choker if you need to).

Improved grab itself seems silent on the issue, though it does mention weight when talking about moving the creature being grabbed which makes me suspect it would be limited:

It can even move (possibly carrying away the opponent), provided it can drag the opponent’s weight.

Does moving a grappled foe through someone’s threatened area trigger an attack of opportunity?

If one has grappled a foe, and then succeeds on a check to maintain it, one of the options is:

You can move both yourself and your target up to half your speed. At the end of your movement, you can place your target in any square adjacent to you. If you attempt to place your foe in a hazardous location, such as in a wall of fire or over a pit, the target receives a free attempt to break your grapple with a +4 bonus.

The attack of opportunity (AoO) rules state that:

Moving out of a threatened square usually provokes attacks of opportunity from threatening opponents. There are two common methods of avoiding such an attack—the 5-foot step and the withdraw action.

  1. Does being moved out of a threatened square by someone else (in general, or while grappled) triggers an AoO?
  2. If it does, would that trigger the "if you attempt to to place your foe in a hazardous location" clause?

How far can you drag a grappled, heavy opponent?

A mostly theoretical rules question. Assume a Medium creature (“Grappler”) has grappled another Medium creature (“Heavyweight”). For unimportant reasons, Heavyweight is very heavy- heavier than Grappler’s carry capacity, but not so heavy as to exceed Grappler’s push/drag/lift capacity.

The rules for moving a grappled opponent (PHB p.195) state:

When you move, you can drag or carry the grappled creature with you, but your speed is halved, unless the creature is two or more sizes smaller than you.

The rules for dragging a weight (PHB p.175) state

You can push, drag, or lift a weight in pounds up to twice your carrying capacity (or 30 times your Strength score). While pushing or dragging weight in excess of your carrying capacity, your speed drops to 5 feet.

If Grappler were to attempt to drag Heavyweight, in what order should these rules be adjudicated to determine how far Grappler could move?