If the spell that's copied is modal (that is, it says "Choose one —" or the like), the copy created by Twinferno's delayed triggered ability will have the same mode or modes. You can't choose different ones.

If the spell that's copied has damage divided as it was cast, the division can't be changed (although the targets receiving that damage still can). The same is true of spells that distribute counters.

You can't choose to pay any additional costs for the copy created by Twinferno's delayed triggered ability. However, effects based on any additional costs that were paid for the original spell are copied as though those same costs were paid for the copy too.

The copies that Twinferno's ability creates are created on the stack, so they're not "cast." Abilities that trigger when a player casts a spell won't trigger.