Keltham has a Commune that - it's risky to use, if people aren't telling him the whole story, if there's kinds of information that Abadar cannot commit not to use, but, Keltham thought he felt, in Abadar's connection to him, that Abadar really wanted him to use Commune, and - there's versions of the story where it could be stupid to ignore a request like that -
Keltham can't actually bring himself to ignore a request like that, if Abadar is a kind of thing that has feelings at all.
Though Keltham doesn't think, of most of the questions he has in mind, that the expected answers to them would matter a lot to Abadar - he'll ask the Pharaoh in writing if there's a better question.
Commune should come before learning about children in Hell, in case that snaps his cleric connection.