Granny Rags and Slackjaw in Dishonored: every choice and what it leads to
Granny Rags and Slackjaw, the boss of the Bottle Street Gang, each ask Corvo for help across three missions, and in the last one only one of them can be helped. Every task below is an optional objective, written as the journal writes it.
What does Granny Rags ask in High Overseer Campbell?
In High Overseer Campbell Granny waits in her apartment. Her objective, Gentlemen Callers, asks you to deal with the men bothering her, then collect a gift from her. She then sends you to break into Dr. Galvani's flat on Clavering Boulevard for a sample of infected rat viscera and to contaminate the Bottle Street Gang's bootleg elixir with plague. The mission's end screen records this as "Helped Granny Infect the Bottle Street Gang".
Her own writing shows why: in a note from Granny she warns you away from "those bad boys from the distillery".
How do you remove the Pendleton twins without killing them?
In House of Pleasure Slackjaw offers the non-lethal route. The journal's tasks are: locate the Art Dealer in the Golden Cat, persuade him to reveal his safe combination, and return to Slackjaw with it. The end screen then reads "Put the Pendletons to Work In Their Own Mine"; the lethal route ends with "Steamed A Pendleton To Death" when Morgan dies in the steam room.
The Art of the Steal asks for both: you
gave Slackjaw the combination but robbed the safe first. Slackjaw's other
request, finding his missing man Crowley in Dr. Galvani's offices and bringing
back the audiograph near his body, is separate from the Pendletons.
Which side do you take in The Flooded District?
The Flooded District offers two objectives that exclude each other:
- Help Granny Cook Slackjaw: incapacitate Slackjaw, get Granny's key, unlock him, put him in the tub, then talk to Granny for your gift.
- Help Slackjaw: find Granny's cameo, destroy it in the furnace, defeat Granny one last time, take her shackle key and unlock Slackjaw.
Does the questline affect Clean Hands or Ghost?
Clean Hands requires completing the game without
killing anyone, and 
Ghost completing every mission after
the prologue alerting no one or killing no one but key targets. The objectives
above name what you must do; they do not say which of those acts the game
counts as a kill, so read each step against those two requirements before you
commit to a side. Slackjaw's past is in
Early Life and Criminal Record: Slackjaw.