At a point during "A Song of Lust and Guile", the Dragonborn sings to Lisette. From her reaction, the Dragonborn is an awful singer. Progessing the quest requires to do the vanilla quest giving membership of the Bard College. What do you do to be accepted? Not singing, or playing an instrument, or writing poetry, or anything bardic, but completing a Dungeon Crawling quest. Of course your singing is terrible: you have been made a bard despite not having your musical/voice skills evaluated, and the game doesn't have any way to attend the lessons at the Bard College.
Once Elisif becomes available as a proper follower at completion of her questline, she can be brought along to fight in the Skyrim Civil War's questline. Legates and legionaries seem indifferent to the presence of one of the higher Skyrim's imperial rulers among their ranks, but why would they recognize her? She wears an armor instead of actual Jarl/High Queen regalia; for most of history, most people didn't know how their rulers exactly looked like (photography didn't exist, paintings were expensive and thus commoners didn't own them)note One of the historical sources which allows to know how rulers looked is ancient money, as current ruler's face was sometimes engraved on coins, but it isn't the case in Skyrim (if the ingame model of the Septim coins is supposed to be taken at face value, the face represents the founder of the Empire). Also, legionaries are the soldiers of an army belonging to an empire larger than the sole province of Skyrim, so Elisif isn't everyone's ruler. The apathy of Tullius, Balgruuf, and Ulfric (who do personally know her) when Elisif is following the Dragonborn is Gameplay and Story Segregation, though.
It might seem odd that the Dark Brotherhood has no quests attached to any of it's members (based on how the mod handles situations like Saadia's, obviously if one was to destroy them, they would be locked out of said romances, but there's no options available if the player chooses to join them) - but then you recall only three members and the player aren't scripted to die during the Pentilus Oculatus's assault. As for them:
Babette may be a case of Really 700 Years Old, but she's still in the body of a child, and even uses that fact to kill several people (not to mention it's implied that pedophiles are acceptable targets for her).
Nazir's relationship with the player stays professional for most of the questline, only really starting to become friendly towards them around the time the Brotherhood is almost wiped out.
That leaves Cicero as the only member who could have a quest attached to him, but since the player chooses if he's Killed Off for Real, he's not guaranteed to be alive by the end of the faction's questline.
Plus, one could say that you're technically in a relationship with the Night Mother (thankfully a nonsexual one).
Dushnamub refers to Bolar and Yatul as his aunts, while they're his great-aunts (they're the aunts of his father Chief Mauhulakh). While this may just be an oversight, the quest where they're all involved reveals Bolar and Yatul have a creepy attraction toward their nephew, so imagining Narzulbur's leader having a twisted, inbred family tree isn't much of a stretch.
