You create and cast the copies all during the resolution of Mnemonic Deluge. You can't wait and cast them later. If you don't cast all three copies, the ones you don't cast will cease to exist.

Because you're casting the spells during the resolution of Mnemonic Deluge, ignore any timing restrictions based on card type. In other words, you can cast copies of a sorcery card this way.

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. If the card has any mandatory additional costs, you must pay those to cast it.

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