The only reason Linux itself is not considered part of the GNU project is... well I'm not even sure. I guess it's partly because Stallman already had his own baby Kernel in the works (Hurd) and because Linus wanted his own brand name apart from GNU, possibly. Also because GNU itself started as a "system" project and that's what it mostly does, except an outsider provided the Kernel and this Kernel doesn't need the GNU userspace to work. Linux is GPL-licensed software.
As far as I'm concerned it's a matter of egos and tags. I personally go with whatever distribution I use, which is a lot more relevant to practical matters. Debian also runs on NetBSD and FreeBSD kernels, by the way.
True. But it's a representative way to describe the aggregation of all those projects (and doesn't promote a single contributor (a very major one, but still one among many) above everyone else the way calling it "linux" does).