We saw that there was an "O. Cobblepot" imprisoned at Arkham in the Elseworlds crossover. I suppose we'll just have to take all the names we saw on the cell doors in Arkham as fun little Easter eggs rather than statements of canon.
No need for that. Cobblepot's mayorship was in the past, and relatively brief judging from Luke's lines; the current Gotham City mayor is Michael Akins. I'd assume Pengy was mayor for a time, then was brought down (no doubt by Batman) and ended up in Arkham.
Hell, wouldn't the fire also use up the Oxygen too?
Well, the mix was 6% HCN, and the atmosphere is about 20% oxygen, so I'd assume the majority of the oxygen would still be left over once the HCN was expended. And the courtroom was locked down, not necessarily airtight.