I'm not quite sure about the meaning of Maury's following sentence: "You see, I felt that we were even denied what consolation there might have been in being a figment of a corporate man rising from his knees." In chapter 3 (The Broken Lute), what is the meaning of "den" in the following paragraph: "The effect on the whole needing but a skull to resemble that venerable chromo, oncea fixture in every den." In "A Matter of Civilization" when describing Camp Hooker, what exactly is “A Mining Town in 1870–The Second Week.” Is it a painting or something else? When speaking about Dot, the author says "made as near an approach to character as she was capable of by walking in another direction," which is rather incomprehensible to me as a sentence.

The first sentence is taken from F. Scott Fitzgerald's The Beautiful and Damned and is in the context of a man feeling generally dissatisfied with his purpose in life and, more broadly, the purpose of people on earth. He has been prevented from making his own choices, and he feels that he has been denied every satisfaction—even the satisfaction of being a "figment of a corporate man" (that is, an image or a ghost of a businessman or a shadow of oneself). He feels constrained, essentially.
"Den," in the context of the second quotation, is another word for a lounge area or living room. It is used differently in different English-speaking geographical locations. Sometimes it means a room used by the man of the household for his private activities and relaxation, but, more generally, it tends to mean a cozy room used by the whole family to watch television, read, and so on. It has a 1970s connotation, and the first meaning of "den" is not used so commonly today.
"A Mining Town In 1870—The Second Week" is not a real painting or photograph, but the phrase is written in the style of a title for a painting or photograph. It is meant generically and refers to the fact that mining towns established in the United States around this time would generally be erected very quickly. Many would have many tents and temporary buildings for the first few weeks. As such, the camp looks as if it is relatively new, it appears rather backwards for the time period, and it appears slightly haphazard in its arrangement of tents and shacks. However, it is functional and industrious.
The comment about Dot is rather unkind, but it is meant humorously. The author is saying that Dot had no personality or character; the only time she ever had a personality was when she walked away—that is, the best thing about her was her not being present. We can infer that Dot is rather boring.