I don't think so. "Territoire Numérique Ouvert" seems to be a private project that would give tools to the "collectivités territoriales" (i.e. mayors and local people).

La Suite Numerique is a bunch of tools for a more global population. It's mostly for government workers I guess but it looks like anyone can use it. The most famous tool is Tchap (see <https://en.wikipedia.org/wiki/Matrix_(protocol)>) which is used by cops in France as a secure messaging platform.

I'm not sure either, but those seem like completely parallel initiatives, with overlapping but not quite identical feature sets.

Almost certainly related. Im sure Lyon won't just use those tools, but im sure they'll also be front of the queue for consideration.

googling a bit (as a french speaker with no specific knowledge about these): doesn't seem like it