Kaya the Inexorable

If you cast a spell “without paying its mana cost,” you can’t choose to cast it for any alternative costs. You can, however, pay additional costs, such as kicker costs. If the card has any mandatory additional costs, those must be paid to cast the spell.

The ghostform counter added by the first ability doesn’t have any functional importance. It’s there to remind you of the ability the creature gains. Even if that counter is removed from the creature, the triggered ability it gains will still work.

If the spell has {X} in its mana cost, you must choose 0 as the value of X.

If a nontoken creature gains more than one instance of that triggered ability, each of them will trigger separately. You can return the card to its owner’s hand only once, but you’ll create a Spirit creature token for each of those abilities.

If you own a face-down card in exile, Kaya’s emblem will let you cast it only if you can look at the card (and only if it’s legendary). If you aren’t allowed to look at the card, you can’t cast it, even if you know it’s legendary.