Are Dooms applied by Cataclysm in Metamorphosis intended to each cost Fury individually?
No, bug.
Is the duration of the debuff applied by Demonbolt updated dynamically with Haste, or does it snapshot Haste at the point of cast?
No, cooldown durations are always set at cast time.
Will Cataclysm be tuned to be on par in terms of DPS with Demonbolt for single target encounters?
No, purely single target, Demonbolt would likely beat Cataclysm.
Will Demonbolt gain some kind of benefit for multitarget fights, where it's objectively inferior to Cataclysm/Servitude-Infernal?
We're aiming to make them as competitive as possible, but at their core, Demonbolt accells at single target damage, Cataclysm at AoE damage, and Servitude at flexibility and simplicity.