Final Fantasy III is set in Hydaelyn's 4th Umbral Era

[HiirNoivl]

Unfortunately, Regarding Eureka, we don't have much to go on.

Eureka is an optional dungeon. You can only get there after "killing" Doga and Unei and receiving the key. The Eureka Key is activated from within the Crystal Tower and you enter. You get the most powerful weapons in Eureka by fighting some enemies. Some were mentioned above. Many of them have parallels with the World of Darkness.

You can see the complete list here.

If the rules of lingual shifts can apply, Kashka could be referring to Kashuan. I don't see any other mentions of Kashka dynasty anywhere. But Kashuan is in the universe of FFII

FFII also has the whole Light / Darkness theme.

Notable places are:

Semitt Falls

Which looks a lot like this from a different angle

But to be honest, Eorzea's history and story seem pretty independent. They can add cute references to other installments ("Wild Rose" password... lol) But to be honest I don't think Eorzea takes place in the exact same dimension/universe as III or II or any other FF in the series.

[Yrusama]

Hiir's idea fits rather beautifully with the Chrono Cross theory I retracted. In this case, Eureka/Hydaelyn and the world of FFIII are the same world, but in different realities. They only have a few crossing points, particularly the doorway in the Crystal Tower.

The existence of Xande in both dimensions could be one of those fated occurrences, as well as the existences of Cid (or a Cid lineage), Chocobos, airships... the works. You could extend the idea to the rest of the series (same world, different realities), but it works rather well here.

I also think that the mother crystal in XIV is not the first time the planet's Aether converged. It's possible that the four elemental crystals were nodes of Aether that gained sentience because the myriad lives collected into complete minds (sort of like complete proteins, needing all of the components of a full mind and will). Otherwise, maybe in Hydaelyn it collects into one mother crystal, and in other realities in collects into four (or in Vana'diel's case, five). This sort of thing happened in FFVII with the Huge Materia, as well.

Edit: treat for you all

[Akujin]

I've been meaning to ask this for awhile. Does anyone have a chart/list somewhere that details each Astral/Umbral era and the key points taken away from each of them. Such as what marked the apex of prosperity and calamity for each of them in turn?

[Catapult]

I've been meaning to ask this for awhile. Does anyone have a chart/list somewhere that details each Astral/Umbral era and the key points taken away from each of them. Such as what marked the apex of prosperity and calamity for each of them in turn?

Not... a proper chart, but we should make one.

[Akujin]

Not... a proper chart, but we should make one.

I concur and I believe you should be the one to throw it together. I would trust you and your mates from these sections to do an accurate job of it.

[HiirNoivl]

Fernhalwes mentioned that the entry points between Eorzea and the void grew much wider and attracted all manner of creatures when Dalamud grew near to it when before it was confined to certain areas of Eorzea such as Dzaemel Darkhold, and Toto-rak. When that happened voidsent creatures cross over, hungry to feed on the aetherrich Eorzea.

And then the wandering Minstrel says this:

Many a night, when I stare up into the boundless heavens, I will oft catch a glimpse of a world not quite our own... Different, yet eerily similar. Is this the Void, or is it something else? I suppose time will tell...

That world not our own, I don't think it's the Void. I feel that the "void" is the World of Darkness, where the Ascians, Paragons, and powerful voidsent come from. Crystal Tower I believe is a gateway that other world. But there are probably others, like where the moogles came from (XII and Tactics), where Bahamut (Maybe from III? or IV? or VI?) and Odin (Maybe from II) came from and where Lightning (XIII) will come from.

[Soul_Blackstar]

Also after defeating Atomos it would drop a weird stone on the ground (was it named Void-stone? can't remember ><; ) and sometimes examine it could trigger a screen blackout/backin with a text saying something like: You had a distorted view of the world. (can't remember the exact text either sorry ._.; ) Could that be the Void too?
I like the idea that the Void can be the World of Darkness, it is a nice fit. (: