You must follow the normal timing permissions and restrictions of each Dragon spell you cast this way.

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.

Once you cast Dracogenesis, if it’s your turn, you’ll have priority immediately after it resolves. You can cast another spell before any player can attempt to remove Dracogenesis with spells or abilities.

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.