Anything not designated with an action is a Psi Like Ability, so a standard action.
Firepower just increases limit, although there a couple of other things it does too.
They can't augment Bolt of Flame.Changed my mind.
Heat Death is a Psi Like, so standard DC of 10+1/2 level + primary ability mod.
Soulfire I just tripped up on.
Conflagration, yes. Both saves.
Sunfire is meant to be a capstone. It's pretty strong, and shouldn't be TOO easy.