The spell is cast during the resolution of Mindleech Mass's triggered ability. You may cast any nonland card in the player's hand, not just an instant card. This doesn't get around other prohibitions, such as "Cast this card only before attackers are declared."

You control the spell and, if it's an artifact, creature, or enchantment spell, you control the resulting permanent.

The card is cast from your opponent's hand, not yours.

You choose modes, pay additional costs, choose targets, etc. for the spell as normal when casting it. Any X in the mana cost will be 0. Alternative costs can't be paid.