Yep, pretty much.

Not exactly fair, but that's the current 'system'..

Yes, and be aware the operation of a lot of ccTLD's are outsourced to companies outside the country in question.

I don't know that much about how many are or aren't operated out of the US, but most of the generic TLD's are, and several ccTLD's definitively are too - for example .tv and .cc are operated by Verisign, and .co is operated by Neustar.

Yes.