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

You cast the copy while the ability is resolving and still on the stack. You can't wait to cast it later in the turn.

If you don't have an enchantment, instant, or sorcery card in your hand, you won't be able to pay Saruman of Many Colors's ward cost.

You don't choose a target for Saruman of Many Colors's ability at the time it triggers. Rather, a second "reflexive" ability triggers when one or more cards are milled this way. You choose a target for that ability as it goes on the stack. Each player may respond to this triggered ability as normal.

If you don't want to cast the copy, you can choose not to; the copy ceases to exist the next time state-based actions are checked.

If the spell you cast has in its mana cost, you must choose 0 as the value of X when casting it without paying its mana cost.