I am writing a novel from the perspective of a character who is very obsessed with Chuck Palahniuk’s “Fight Club.” This is essential to the character and can’t be changed, but I can (and will, obviously) change the execution if necessary. I understand that allusions are acceptable in literature, but while tuning into this characters thoughts and writing in their voice, I seem to be quoting Palahniuk’s book a lot? ie,”a copy of a copy,” “if you wake up in at a different time in a different place,” etc. I’ve been putting my own spins on these quotes to convey my own ideas, and I’ve made it very clear that this is a reference to someone else’s work so as to not accidentally claim it as my own, but before I get too deep into writing this novel, I want to make sure I’m not doing anything that would be considered stealing or even illegal…
It might be violating copyright. Just giving credit to the original author does not cover you. They own the right to their words, especially identifiable phrases (unless you can find those phrases in work previously published before their work.)
You must get permission from the owner of the copyright (writer and/or publisher) in order to use their unique phrases.
Otherwise, they can sue you, and for a famous work, probably will.
The title is fair game, that is not copyrighted. But character names within the story may also be trademarked. For example, you cannot use "Harry Potter" without violating JKR's trademark on the name (for use in a commercial product).
Other than the title, the answer is NO. Giving credit does not absolve you. You cannot use their words to make money in any way.
Now, plots are not copyrighted. You can steal a plot, and reimagine it. But you cannot steal phrases or sentences or paragraphs, to use in a commercial product, without permission.
There is a "Fair Use" policy, for the purpose of critique, commentary, news reporting, teaching, scholarship, research or parody.
Notice that those do not include novels or movies (unless they are parodies).
If using their words improves your work, then you are making money from their words in basically the same venue as them, and you don't have the right to make money off of their work in the same venue as them.
There may be some legal exceptions, but I wouldn't work so close to the edge.
And as an unpublished author, it will be extremely difficult for you to get permission on your own own, and I doubt any publisher will consider an author's first book that comes with legal work to do.
Don't use quotes directly from a copyrighted work, unless you can find them in some other works published before theirs. Period.
TL;DR: What you're describing is considered transformative work. As such, you're not doing anything obviously illegal, and you can set aside legal questions to deal with in the editing and publishing process.
The U.S. Copyright Office Fair Use Index says, "Transformative uses are those that add something new, with a further purpose or different character, and do not substitute for the original use of the work."
Other considerations include how much of the original text you use; whether sales of your book would harm sales of Fight Club; and whether your work is using the material creatively. (For example, having a character reference Fight Club all the time, as part of a character arc that echoes themes in Fight Club, might be more likely to be considered "creative expression" than having a character whose sole personality trait is quoting Fight Club.)
Stanford has a great guide on what those standards are and how they're applied. But the biggest takeaway from that guide, as far as your situation is concerned, is that specific publishers each have different policies.
Fight Club was published by W. W. Norton. Their website isn't very helpful; instead of a published fair use policy, they just have instructions on asking them for permission.
However, I came across a panel from a biographers' convention, where John Glusman, the editor-in-chief and vice president of W.W. Norton was one of the speakers addressing fair use. Some of the information was specific to writing biographies (like the need to quote important evidence for your assertions), but I think this excerpt applies well to fiction:
"Scholars have shown, repeatedly, that if your use is 'transformative,' you will win in court.... Courts have become quite willing to dismiss cases at early stages when a strong fair use case is evident on the face of the complaint.
"Fair use makes books better. Arbitrary omissions and alterations that are rooted in legal fear, rather than in the author’s (and the editor’s) judgment about what best serves the story, will always make a book worse.... "The publisher that is willing to flex their fair use rights in support of authors will publish more, better books, and they will attract authors who value the freedom to tell their stories to the fullest extent allowed by their First Amendment rights, rather than having to trim their sails in deference to illusory legal risk. For a while, this will give savvy publishers a competitive advantage.
"According to Congress, fair use is a right, and the Supreme Court has weighed in to say that it’s closely related to the First Amendment freedom of expression. So, there is nothing sneaky or disreputable about exercising the fair use right where it applies.
"Experience in other fields suggests that once one publisher or editor takes advantage of their rights, others will follow eventually, lest they be left behind. As more join the fair use pack and industry norms catch up to legal reality, there will be safety in numbers and everyone will be better off for it. For this to happen, though, authors may have to take the first step, by insisting that the editors and publishers allow them to make responsible use of this important copyright doctrine."
Glusman wasn't quoted directly; that's just the gist of the panel. But the fact that he was on a panel which gave this overall opinion implies that he, and W.W. Norton overall, are okay with it, whether or not he's the one who specifically stated any of it. (You might also be able to watch the recording of the panel at that link.)
All of the above applies even if you quote Fight Club directly. From what you described in "putting your own spin on it," I wasn't sure whether you were ever quoting Fight Club directly, or if you were sort of writing your own versions of the quotes. It sounds like your work might be better-served by just quoting it, at least some of the time -- but more than anything, this sounds like it should all be a creative choice right now.
Do what works best for the book: not only because that makes a stronger argument for fair use, but because that'll make a stronger book.