Bone Skewer

Yes. The unit's untargetability ability is inactive while the card is in hand, and Bone Skewer's choice does not target it.

"I can't be chosen by enemy spells and abilities" is a passive untargetability ability.^757757.1 Passive abilities of permanents are typically active only while they are on the board.^365.1 An ability that functions in another zone describes that context itself,^366.1 which this ability does not, so it has no effect in hand. Separately, a card in hand is not a target because the hand is not a public zone.^355.10.a

Yes. The reflexive trigger that stuns the unit does not ask its controller to choose anything.

If the opponent plays the unit, Bone Skewer's "then do this" wording creates a reflexive trigger.^388.1388.2 The trigger is linked to the preceding ability, and "it" can only refer to the unit played by that ability.^395.1398 The unit is therefore programmatically determined rather than chosen by the trigger's controller, so it is not a target.^{355.10.d355.10.d.1}

Untargetability does not prevent the stun because it only prevents the unit from being a legal target.⁷⁵⁸

No. Hide is a separate action, not a way to fulfill Bone Skewer's instruction to play the unit.^811.1.c.1 Bone Skewer instructs the opponent to play the unit as a limited action, following the normal play process except where the effect says otherwise.^420.3420.3.b

Yes.

The phrase "any and all costs" in Bone Skewer's text is broader than the standard "ignoring its cost" wording. Standard cost-ignoring only zeroes out a card's base energy and power costs.^356.1.b.1

1. The opponent chooses whether to pay an optional additional cost while making the relevant choices for the unit.^355.1.a

2. A chosen additional cost is included when determining the unit's total cost, which Bone Skewer then sets to zero.^356.2356.5.a

3. The optional additional cost counts as paid based on that decision, regardless of the amount actually spent.^356.4.f.1