-Is it true that there is no other way an individual can reach an independent economical status without being part of a chain-reaction type of exploitation from other people, as Socialism claims?
It depends on what you mean by "independent economical status". The only way to be truly independent of the rest of the economy is to be alone on an island.
-Is it true that this "exploitation" that Socialism criticizes is actually an exploitation per se or is this relative? (Especially considering that no one's being held a gun to their head and forced to work for a company)
I'm not sure what you mean. Having a gun to the head was never a central argument of it all, so I have to wonder.
The fact is, it goes kinda like this: let's Joe, Tom, Dick and Harry make their own late 19'th century style car workshop and make 2 cars. Joe takes one car 'cause he's the boss. Tom, Dick and Harry get to carpool in the other one, 'cause they're the ones who actually hammered metal. Is it a fair distribution of the result of their work? Does it really matter if Joe held a gun to their heads, or just talked them into being shafted, or there was some other kind of setup?
But in RL situations you have CEOs who get 1000 times as much as the guys at the assembly line. Even when they're driving the company in a death spiral.
The fact is, money don't exist in a vaccuum. For the purpose of wages, it's just a way to divide the pie. A million people make a huge pie, and they get vouchers for how much of it they can take. That's money in a nutshell. And some guy gets to take 1000 times as much as the next guy who put the same 8 hours into it. WTH did he do for that? Crap golden eggs? The fact is, it's only possible because there were other people chipping in some work to make that 1000x portion possible. That's exploitation.
Gun to the head is a red herring. We created a system where that's the only choice, even without guns involved. The farmers still plough, the bakers still bake, and builders still build houses for them, but somehow they have to make a banker or VC rich in the process too. They may not have a gun at their heads, but they live in the system where most available choices boil down to the same thing, and they _have_ to pick one. Because that's how the system works.
And then some of us think it's high time to fix the system a bit.
-Is it feasible to conceive of a society that has no division of classes, where everything is equal or does this ignore some basic aspects of human nature that would make this an Utopia?
Nature? No. Other societies functioned perfectly well in cultures of sharing. The bushme, potlatch cultures, etc. Even in Europe before Adam Smith greed was a mortal sin, not something to flaunt and get social status out of.
Nurture? Yes. That's the culture we live in, and that's the kind of behaviour we learn.
Unfortunately, it boils down to largely the same problem. Culture turns slower than a battleship, and if you push too hard, it actually starts pushing back. It's not particularly realistic to have a plan that involves radically changing the culture, as the USSR amply proved.
So, yes, we'll never really be classless. That much is very much clear. Yes, some guys will have to take a bigger slice than other guys. It's what motivates people in this culture. But we can at least see to it that some people don't get entirely trampled up in the others' rush for gold.
-Is such scenario actually envisioned by Socialism, or is there always a certain type of class division no matter what?
Depends upon which definition of socialism you use. In the USA the term has been hijacked to be largely a synonim for communism. In Western Europe the aim is more like just to reduce the inequality a bit more.