The only "condition" that Destiny Hero - Diamond Dude's effect cannot ignore is when the Normal Spell has a specific window for activation.
"Curse of Fiend", while a Normal Spell, is only activatable in the Standby Phase (which is not a time Normal Spells can normally be activated). Since Diamond Dude's effect only works in Main Phase 1 or 2, it could not activate it. If "Cold Wave" was sent, that can only be resolved as the very first thing to be done in Main Phase 1. If you did something else or are in Main Phase 2, Diamond Dude's effect could not use it.
All other conditions (based on Monsters on the field, costs, and so forth) that are not based on a specific Phase or Timing in a Phase are otherwise ignored. So Diamond Dude can fire off "Des Croaking" without any issues.
