But yeah, you're right, what I'm doing is trying to make some sense out of why Sithis answers prayers, because the working altar of Sithis is, whether people like it or not, canon, since it was in the game.
Actually, I don't think so. That altar wasn't in the game proper, but was, rather, one of the "official" DLCs. While some of them complete an interesting area of the setting (the Orrery springs to mind), others, such as the "alter for evil people" were little more than purchasable cheat codes with flavoring. It wasn't in the original game, it wasn't included in GOTY. As such, I consider it to be no more "canon" than a player-made expansion.
As for me, I draw the relationship between the Dark Brotherhood and Sithis from the book bearing his name: Sithis. In the beginning, Sithis shattered the nothing, ideas came to be, enjoyed a finite existance, and went. That is, from a Sithic point of view, the way things should've been, but certain spirits had other ideas, and manage to extend their existence beyond what was "proper". Lorkhan was introduced, to bring mortality to these beings, to some degree of success.
However, the same problem Lorkhan "solved" on a mythic scale came to exist in this new world. While most people came and went as they were supposed to, there are certain lineages, institutions, etc. that seek to extend their existence beyond what is proper, that are able to enlarge and extend themselves by devouring others. Enter the Dark Brotherhood, another Spawn of Sithis, just as Lorkhan was. Institutionally speaking, they kill for money.
However, they introduce an element of chaos into the efforts to strengthen institutions to live on beyond their creators. Though all individuals eventually meet death (certain exceptionally powerful mages excepted), the institutions they create can live on. If, however, an element of chaos, a happy band of murderers who will (and moreover,
can) go after anyone if asked, is introduced, these institutions are destabilized.
In short, Sithis "favors" the continual flow of life and death, the limitation of existence, and acts to counter any efforts to break those limits. On the stage of Myth, Lorkhan serves this end. On the stage of Society, the Brotherhood serves this purpose.
Note that this only comments on the "behavior" of Sithis. It still doesn't explain what Sithis
is.