Belah'dian Red Mages?

So I was looking at a list of the Red Mage Weapons and noticed a weapon called Belah'Dian Degen which is found in the Gubal Library. I noticed a lot of the Gubal Library weapons seem to be old historical weapons, for example the Pre-imperial Garlean Revolver or the Royal Nymian Marine Codex, and Royal Nymian Marine Battleaxe.

1. Was Belah'Dia founded shortly after the flood?
2. Was it around the same time as Ala Mhigo was founded?
3. If so Was Belah'Dia made up of Amdapori and Mhachi as well which could have founded a second Group of Red Mages?

Belah'dia was founded as a refuge for mages from persecution. It's possible some Red Mages traveled there.

Gubal Library is basically a collection of ancient knowledge and artifacts. I would not be surprised if that place holds a weapon for maybe future Jobs as well if SE plans to have level 50 to be the default starting level for all future Jobs from now on.

Seeing as how Red Mages used to be a huge group of them but then dwindled down to nothing, until the the kitty and stuff decided to use it to rebel against the empire... It wouldn't surprise me much

Belah'dia is the ancestor city to both Sil'dih and Ul'dah, and was founded sometime after the flood that ended the War of the Magi, so it's possible there were some Red Mages there at some point before its own split.

Just my speculation but there was once a class planned for the game back in the original 1.0 version of FFXIV called 'Fencer' (FNC for short) that was never implemented (references to 'Fencing' as an weapon ability style existed in 1.0's files but were dummied out) which RDM effectively inherited as a weapon type (like how MCH inherited the equally never implemented Musketeer class lore and weapon type). So this is a wild guess but it's possible the never implemented FNC might have had it's lore origins in Belah'dia and died out to be forgotten, and RDM merely picked up this forgotten weapon type and modified it for their own use.

But that's just my musings so take from that what you will. ;)