"Neoliberalism" is just an Americanism for economic liberalism, because the word liberalism is overloaded in the U.S., and is an autoantonym. That part of vezzy-fnord's comment is just a reflexive libertarian expulsion.
Not sure at all -- a lot of critique I've seen directed at "neoliberals" (and the term is exclusively used by critics), seems to target policies that are decidedly non-libertarian.
It is always used to critisize things from the left, which creates an impression that the term describes economically right-of-center ideologies, but that's IMO just because of the difference in vocabulary between different groups -- e.g. you may see the same thing described as neoliberal by the left, liberal by the right, and "statist" by the libertarians.
Thinking about it, "statist" is a similarly empty term used exclusively by opponents -- I've never seen anyone calling herself a "statist" either.
