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.