Vivi was constructed artificially, but he's still a living being. The potential for reproduction could well exist, either buried in his physiology or as an inherent part of his design.
Yeah, I'm pretty sure he's dead. He didn't die, like, as soon as the final battle was over, but he died some time after popping out a few mini-hims.
Perhaps they are not literally his 'children' that he spawned with another black mage (as they all seem to be male, as far as I can remember). Like what was mentioned earlier, I think he found a way to make more black mages, perhaps with longer lifespans or something like that...
But yeah, he is definitely gone at the end of the game...that's what the long emotional letter to Zidane is about.
The Crystal shed its light silently...
Who knows. :eiko: