I'll try to answer since tsukune won't be on for a bit yet, I'm pretty sure.

I think the way we figure unique weapons would be relevant to your specific world. We discussed that the world is unique to the specific character or characters trapped within. From discussing the way the worlds are meant to work, I would assume that the world would take what was in that person's specific world and keep it constant. If the worlds crossed over, there'd be multiple forms of the same weapon, depending on the game it comes from.

If tsukune wants to add to that, he can. We never talked about specific unique equipment. What we DID talk about in more depth was the other thing you brought up. The issue of multiple characters (Cid, Biggs, Wedge, etc) and multiple summons that remain constant throughout all the games. I'm pretty sure what we decided on that front was that the characters act by a kind of multiverse theory. They all exist the same with all their unique quirks that make them different from the others. Summons are a little bit less complicated than that. We treat them as ethereal beings on a different plane than the players. So they are still there and, for the purposes of the stories, I think they would appear in the specific worlds in the way those characters would normally have seen them.

I think tsukune can give a more definite answer than I can, but that's what I understood while talking to him. Just thought I'd answer since I'm pretty sure it's the dead of night where he is currently. xD