A monocolored card is exactly one of white, blue, black, red, or green and no other colors. A colorless card isn’t monocolored.

If you find only one card, you’ll shuffle it into your library and exile Emergent Ultimatum without casting anything.

If you wish to cast any exiled cards, you do so as part of the resolution of Emergent Ultimatum. You can’t wait to cast them later. Timing permissions based on a card’s type are ignored.

Emergent Ultimatum is still on the stack while you cast the cards you found, so those spells could target it. However, once it’s exiled, it will no longer be a legal target.

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 spell has any mandatory additional costs, those must be paid to cast the spell.

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