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After hearing details about Cockbill Street, it suddenly makes a lot more sense that Vimes has always been described as short and skinny. Severe malnutrition in childhood does tend to have that effect.
When Sam Vimes thinks of Stoneface Vimes, he quotes from Stoneface's Journal: "In the fires of struggle let us bake the new men, who will not heed the old lies." This is exactly what Sam Vimes does in the end, telling Carrot to rebuild Dorfl - Dorfl is destroyed in a fight, baked in fire in a pottery oven, and he does not heed the old lies - he knows he can own himself, doesn't need to have a master, and doesn't believe religion to be important even if gods do exist.
Dorfl states that when he is off duty he will debate the existence of gods. A few pages earlier, he tells Vimes that because he does not eat, sleep, or need to bury his granny he needs no time off. Meaning, the next time he will be off duty will be when he is dead and can debate with the gods directly.
Sooner than that, though—Going Postal establishes that every free Golem gets one day off per week.
The effect of Carrot putting his receipt for Dorfl the golem in Dorfl's head is obvious when you look at the exact wording of the receipt: "I Gerhardt Sock give the barer full and totarl ownorship of the Golem Dorfl in xchange for One Dolar and anythinge it doz now is his responisbility and nuthing to doe with me." Dorfl was given new words to obey, words telling him that he owned himself and that he was responsible for his own actions. This sudden introduction to the concept of philosophical agency is a Disc-shattering revelation to someone who's been unable to do anything but take orders from a master for his entire existence, so it's no wonder Dorfl went a little crazy and raised a ruckus.
Vetinari admits to Drumknott that he had the poisoned candle trick figured out ages before anyone else... meaning that he is directly responsible for the deaths of William and old Mrs. Easy, and could have spared them at any time if he hadn't been so patronizingly intent on letting Vimes "have his fun". But there is no indication that he knows or cares about their deaths, while the fact that Dragon and Carry didn't know or care about the deaths of little people inadvertently caught up in their schemes is used to illustrate how monstrous they ultimately are.
Not necessarily—Mildred Easy is sent for to go home the day before the funeral, presumably because her family members are already dead or taken ill, meaning that she'd taken the poisoned candles to them at some point before that. Her absence from the palace is only revealed as Detritus and Vimes question the servants in a scene immediately following Vimes being summoned back because Vetinari's condition has worsened. Since Vetinari doesn't actually allow himself to continue to be poisoned once he figures out the source, he clearly hasn't by that point, meaning that in all likelihood, Mrs. Easy and William died before he knew.