By my reading, it doesn't replace the damage. It's in addition, every single day, compliance or no. I guess this makes sense under the principle that a baleful geas is a geas but always baleful, which this certainly is.
It's definitely, unequivocally a standard action.
Per Draconomicon it is unambiguous that having to wait 1 round coincides with being able to use it again next round. DFA unambiguously can make breath attacks at will, and Power Surge unambiguously gives it a 1 round waiting time.
Thus you are absolutely able to use it again immediately next round. It doesn't appear this is disputable in terms of the rules as written, only as intended. And I'm not certain enough that the intention is otherwise; it at least prevents the use of Quicken Breath to breathe twice in a round.
The party wouldn't find this out naturally unless they had Skall as a patron, but the serial killer would get grabbed, subjected to terrible necromantic rituals by Skall, then killed.
From the party's perspective, the Dustmen honor their word and direct the party to Sofie, and the rest follows. The party will also end with good relations with the Dustmen, which I'll keep in mind for the upcoming campaign. I will suppose that the party then is OK with Sofie dragging Teru's soul gem up to Celestia and find some god or goddess willing to assist, or potentially to Everwatch to be held by Helm if she's dissatisfied with the options.
Five Pebbles was basically being readied for decommission after sustaining substantial damage on Dymos and was in no state to be flown again, not without an artificer to rebuild it. Hence none of the facilities working.
This is likely beyond the scope of a wish's power (being at least as potent as a mass variant of mindrape, a 9th-level spell). Thus the wish would have a very large scope of possible drawbacks to "balance" affairs that a solar would be unwilling to test.
The Grand Sultan is an epic caster, it seems unlikely to be beyond his reach unless in the domain of another epic caster or deity. Sofie might recommend sending Pilot over to Akadi's court, or to the court of the Great Caliph of Air, who is not statted but likely epic or even possessing divine ranks. Pilot would probably resist the latter on political grounds, and would want to avoid the former if possible to avoid become a servitor—with his freedom recovered, he is loathe to give it up again—but when Sofie impresses on him that he is likely to die otherwise and the party unwilling to intercede and speak to the Court of Fire, he would crumble and accept a new life in Akadi's realm.