If the card has X in its mana cost, you must choose 0 as its value.

The card goes to its owner’s graveyard after it resolves (or otherwise leaves the stack), not yours.

If you cast a card “without paying its mana cost,” you can’t pay any alternative costs. You can pay additional costs such as kicker costs. If the card has mandatory additional costs, you must pay those.

You cast the card from the opponent’s hand immediately. Ignore timing restrictions based on the card’s type. Other timing restrictions, such as “Cast [this card] only during combat,” must be followed.

Any player can respond to Mindclaw Shaman’s triggered ability. However, once that ability starts resolving and the target opponent reveals their hand, players can’t respond until after the ability finishes resolving. For example, the opponent can’t cast the instant or sorcery card you choose to cast in order to stop you from casting it.

If you can’t cast any instant or sorcery card (perhaps because there are no legal targets available) or if you choose not to cast one, then Mindclaw Shaman’s ability finishes resolving and the game moves on.