The copies are created and cast during the resolution of Mizzix’s Mastery. You can’t wait to cast them later in the turn. Timing restrictions based on the copy’s type are ignored. Other restrictions (such as “Cast [this name] only during combat”) are not.

If you don’t cast one of the copies (perhaps because there are no legal targets available or you don’t want to), the copy will cease to exist.

If Mizzix’s Mastery exiled multiple cards, you may cast the copies in any order. The last copy you cast will be the first one to resolve.

Mizzix’s Mastery is still on the stack as it resolves. If you pay the overload cost, Mizzix’s Mastery won’t be exiled or copied.

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.

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

The cards remain exiled no matter what happens to the copies.