On the second page, Death explains that Rhea's destination is unknown, and that he has to figure it out manually. However, on the fourth page they already have an appointment (with Buwaro) in the Ring of the Slightly Damned that they are in danger of being late for. Note that vanishingly few souls go there, so Death couldn't possibly have just guessed.
Death dropped in to see Buwaro in hell every other day while they were down there. He was probably doing that well before Rhea showed up.
Angels have their own language, which is a plot point several times in the form of a language barrier. So why do demons all speak Lingo like Medians, instead of speaking Black Speech?
Its to be assumed that Demons have more interaction with Medians than Angels do, as the demons have the role of torturing the sinful ones, while the Angels have no obligation to interact with Medians at all.
It has been stated as Word Of God that Demons were too chaotic to make their own language, so they simply stole it from the Medians.
Stomping on Rhea's tail
Why does Buwaro stomp on Rheas tail? He seems actually evil for a second, then turns back to a lovable moron. What happened?
He was just trying to immitate the other demons, after he got friendly with her, he probably just forgot that he's suppose to torture Rhea as an advisor.
Clothing in Hell
Where does it come from? It's been confirmed that Sakido, Iratu, and Buwaro all changed their typical ensembles at least once, and this could be attributed as Darius getting new clothes for them, but where would one even get it from? And what about other demons, like Azurai? Is there some kind of Hell Spawn clothing store that we haven't seen yet?
How the hell did Azurai qualify for the Ascension? He's an insubordinate loose cannon, constantly undermining his comrades' efforts with his utter lack of restraint for his temper and bloodlust. He has yet to demonstrate any redeeming qualities or useful skills to justify his position; sure, he seems to be rather proficient at murdering people, but all of his victims so far have appeared to be average, unarmed and relatively harmless Medians, and slaughtering helpless people isn't exactly an uncommon skill among Demons. And he doesn't stick to slaughtering only Medians, as his assignment to the senile old man in his first appearance in Hell was implied to be a punishment for casually murdering a Demon classmate. Even assuming that murder isn't that big a deal in Demon society, it's still not exactly the most productive behavior if you're trying to work together to accomplish some goal, especially a covert mission like the one Iratu and co. seem to be on. Sending someone like Azurai is a pretty baffling choice.
It's probably too soon to judge just how important their initiative is since we really have no freaking idea what the heck Iratu and his cohorts are trying to do, but maybe Iratu put in a good word for Azurai back in hell, because he specifically wanted him to come along, for whatever reason. I can agree with you in that I have absolutely no idea why anyone would want Azurai to help them with any sort of important mission, other than his delightfully disturbing talent for making people cease living, but I suppose that will be revealed in time. Or heck, maybe Chu just wanted to bring him back into the story. Who knows?