Right, that's illegal. Management is under no obligation to accept any particular set of terms, but they're also not allowed to just say "nope"; they're required to continue negotiating with the union until an agreement is reached.
So if me and my 2 other buddies are the only two employees at an early startup we can unionize and demand immense equity packages, and the company is prohibited from hiring additional employees if they don't like our demands?
This does not sound right - this effectively gives unions the ability to extort companies with impunity. I'll believe this claim that companies are prohibited by law from hiring a non-union workforce if you back it up with a source.
Correct, firing someone for trying to unionize is illegal. It is illegal to retaliate against workers for trying to unionize. It's not prohibited, to the best of my knowledge, to receive a contract from a union and say, "these term's aren't competitive, we'll find other workers". Otherwise that would effectively give unions unlimited power over companies.