Per the racial / heritage quests that we do have, charred meat(s) seems to be a favourite among the dark iron and their dogs.
Their cultural beliefs and such is a bit open, what we do know is that it’s a sorcerous clan, with an affinity for craftsmanship, masonry, and blacksmithing, who by in large culture was squashed/painted over by the hatred stoked by the Firelord as he enslaved them after their folly.
There does seem to be a new age of belief in the mountain, which appears to be based on a more shamanistic belief of the spirit? At least that’s what I divined from clicking the various NPCs around the Blackforge who claim to speak for the mountain.
As for what to believe as a Paladin, I suppose it really depends on which way you want to take them. - As you mentioned, you could take them to their zealous zenith and have them be some sort of Paladin of the Law, specifically the Ring of Law, adhering to strict oaths and rules of the Emperor and the dark iron nation, with your faith being fiery justice against those who’d usurp the dark iron rule?
You could also go the Doom Dragoon route (The only NPC afaik) that had any light abilities, who seem to be officers of the dark iron nation’s army, who use both guns, light to heal and shield themselves etc.
Or you could be a new-age (After joining the alliance) dark iron paladin, who’s adopted a more human-esque belief in the light after all humans seem to have some ties to the dark iron nation, what with their proximity, as well as the few mentioned characters getting bestowed weapons of renown for Reasons. - Not to mention being the landmark of where Anduin Lothar fell, one of the biggest human knights in human history, who was avenged by a Paladin that struck down Blackhand (If memory serves right).
That’s at least some ways I could think of taking it! x)