How to understand the phrase here

Yeah, in this case “the same fan” and “her” both refer to the same person, who I assume is Vavra here. As for your second question, I think you’re trying to ask if that part of the sentence can be reworded into “…that it was a risible fraud.” There is probably some way to have the sentence keep its original meaning while wording it this way, but you’d have to move a lot around, and in this case there’s a specific construction being used that you’re bound to see a lot in writing. The sentence is saying that the boys exposed the world, showing her it was a risible fraud. The “…exposed for the ___ that it was” construction is just a more natural way to phrase it. As an example, “They exposed the company for the scam that it was” = “They exposed the company (and showed it was a scam)”

"that it was" is a confirmation statement that what the boys said accurately describes reality. To explain more fully, they said that it was a laughable world about personal gain at the expense of others. And what they said was an accurate description of that world.

As a native, I have no clue what most of this says Never has anyone ever used the words profundity, risible, or proselytization. Spellcheck didn't even recognise that last one when I typed it. Ignore those words. But anyway, yes the "her" refers to the fan, the reason why this is here is because the "that same fan" is who the chance of survival was offered to, and the "her" is making it clear that it's HER chance of survival, meaning that it is a chance at her surviving. You could also just say "offered that same fan a chance of survival", but that doesn't sound as fancy, and this author clearly wants to sound fancy. And the "that it was" is a description of the thing before it (risible fraud). The description here is that the risible fraud exposed is the risible fraud, which is just saying that it has been shown for what it is. I still have no idea what "risible fraud" is in case you were wondering.

they offered the fan a chance of survival the world that she lives in is a fraud

They offered a woman a chance of survival. This woman was a fan, soecifically, the fan that was mentioned earlier. The fraud was exposed. It was exposed in such a way that other people specifically now knew that it was a fraud. (As opposed to exposing it, and people not being 100% clear what it was. e.g. it could be a fraud, you expose it as something suspicious, but not conclusively to be fraud).

Just do what I do as a native speaker and NOT understand.

The writer thinks that it's so fraudulent that xe finds it funny, ie it's obviously, clearly, fraud. Adding "that is was" emphasis the author's opinion.

What you're reading here is very difficult. I would expect it would be college level reading for americans. > Is "the same fan" and "her" describing the same thing? Yes, both refer to the same woman. I'm sorry but I don't understand your second question. Risible is a fairly rare word. You could re-write the sentence as: "...how they offered that woman her only chance of survival in a world that was a risible fraud" ...but some of the nuance is lost. I hope that helps though.