“Curse of Darkness” inflicts 1000 damage right after the Spell Card is activated, not when it resolves. If the Spell Card’s activation is negated however, such as with “Magic Jammer”, then no damage is inflicted because the activation was negated.
“Curse of Darkness” does not form a new chain and cannot be chained to. You can chain to the Spell Card itself, after “Curse of Darkness” inflicts its 1000 damage.
Even if your opponent targets your face-up “Curse of Darkness” with “Mystical Space Typhoon”, he/she takes 1000 damage before “Mystical Space Typhoon” resolves and destroys “Curse of Darkness”.
When “Curse of Darkness” is active, and you activate “Double Spell”, you take 1000 damage for activating “Double Spell” but not for the target of “Double Spell”, because it is not considered “activated”.
If you send “Curse of Darkness” to the Graveyard as part of the cost of “Emergency Provisions”, then “Curse of Darkness” is no longer on the field immediately after activation of “Emergency Provisions”, and “Curse of Darkness’” effect is not activated.
Netrep Rulings:
If more than one “Curse of Darkness” is active on the field, a player activating a Spell Card will take 1000 Damage for each active “Curse of Darkness.”
You cannot chain to Curse of Darkness’s effect dealing 1000 damage, because it is a Continuous Effect. Naturally, you can still chain to the Spell Card, of course. This means that chaining the activation of Curse of Darkness (flipping it face-up) to the activation of a Spell Card will not inflict any damage because Curse of Darkness was not active when the Spell Card was activated.