• Can anyone on earth use this network?

Yes.

• Can a state actor take it down?

Yes. But that's true for any blockchain project. Even Monero. Especially something like Eth where the majority of staked Eth is controlled by companies in USA jurisdiction.

• Can big tech override the system for it's benefit?

Yes, if they buy enough of the Token. True for all blockchains. For Solana this is a weakness if big tech wanted to evict from datacenters.

• Are the changes from a few consequential to all without appeal?

Again, true for all blockchains. Name a crypto project, and I will point out that the vast majority of voting shares on in a few hands.

• Is it possible for anyone to claim a piece of this network?

Yes.

• Even if I have less than others, will my node or voice still be heard?

No, not really. Again same with other blockchains.

• Is it possible for a middle class person in a "1st world" country to this run a validator or node for this network?

Yes. Threshold is hire, but certainly possible for a technical person to run their own Solana validator. The difficult part is getting the stake to make it profitable.