Exactly. The OP correctly argued that libre practically implies free-as-in-beer, but I think the point of the distinction is to argue that free-as-in-beer doesn't imply libre. So it's a useful distinction.
This is certainly true. It's very much possible (and common) to give away software without giving away any rights to it.
If that was the only point GNU was trying to make, I'd be in full support.
But that doesn't seem to be their only point. As I read it, they're arguing that freedom-of-speech does not imply freedom-from-cost. And I think that's nonsense (again, after the first sale).