There are very few people actively trying to prevent lower class people from getting into the upper class, but it's competitive to be in the upper class and there are only so many spots. You don't get to be prestigious by letting everyone in.
The plus side is that if you are from a lower class background and somehow overcome your environment, the admissions committees are tripping over themselves to let you in.
Yes, again, that's the point. The entire paradigm exists to justify the unjust concentration of power and wealth in a small upper class. It doesn't require an active conspiracy, it just requires people to accept that there is something objectively 'right' or naturally ordained about this state of affairs, as you apparently do.
I don't necessarily disagree with your points but it doesn't matter. It's a medium-is-the-message thing: when the medium is ideological rhetoric, the message is the death of this forum. What the ideology actually is is secondary.