| Quote #1
Barber Ivan Yakovlevitch, a dweller on the Voznesensky Prospekt (his last name is lost now—it no longer figures on a signboard bearing a portrait of a gentleman with a soaped cheek, and the words: "Also, Blood Let Here") […] Raising himself a little, he perceived his wife (a most respectable lady, and one especially fond of coffee) (1.1)
An amazing run of totally random, highly specific, and at the same time completely useless ways to identify people here. We've got the barber, who gets a profession, no last name, and a super-detailed description of his shop sign. Then there's his wife who gets a super-vague description ("respectable lady"—that could mean anything!) and a detail that really doesn't amount to much of anything ("loves coffee").
| Quote #2
[The barber] realized that the nose was none other than that of Collegiate Assessor Kovalev, whom he was shaved every Wednesday and Sunday. (1.9)
The joke is either the idea that the barber could actually identify a nose without a face attached (who could possible actually do that?), or that the barber is exactly the kind of person who could identify the nose since he has to hold each man's nose during a shave. You pick what you think is funnier. (And of course, nothing makes jokes funny like a long and drawn out explanation of their humor. You're welcome.)
| Quote #3
Like every decent Russian tradesman, Ivan Yakovlevitch was a terrible drunk. What's more, even though he daily shaved the chins of others, his own was always unshorn, and his jacket (he never wore a topcoat) was piebald—that is it was black, but thickly studded with grayish, brownish-yellowish stains—and shiny at the collar, and adorned with three drooping tufts of thread instead of buttons. (1.18)
Here's another bit of character description that starts out pretty normal and then just totally careens off the rails. Remember, we're working with the 19th-century tradition here, where the general rule is that every time a new character is introduced, the narrator does a head to toe, backwards and forwards, origin story and emotional issues type of reveal. Which is kind of how we start out: the barber Ivan is a drunk, which is a national pastime for men of his age and class in tsarist Russia; he doesn't take care of his appearance or his clothes, which is definitely supposed to tell us something about him as a person (go ahead, list the things meant to be revealed by that). But then we veer off into crazy town—the barber is cynical, the narrator tells us (Ahem, big money word here! A cynic is someone who is scornful, jaded, and generally thinks that people are motivated by greed and self-interest rather than integrity)—and what supports this idea? The fact that the dude whose nose he finds has sometimes told him that his hands smell? What?!?!