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

A Giant card is a creature card with the creature type Giant. Presumably, it will be the same size as all your other cards.

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.

If you cast a spell using Surtland Elementalist’s triggered ability, you do so as part of the resolution of that ability. You can’t wait to cast the spell later in the turn. Timing permissions based on the card’s type are ignored, and the spell will resolve before blockers are declared.