To answer your question about them all being linked, I highly doubt it from a XIV players standpoint. However, to fill in some of my experiences with the game's lore, the 7th Umbral Era is the end of a life cycle when the planet is essentially about to restart and life is reborn once again, pretty much wiping out all life currently known in existence.

But of course, this can be interpreted in different ways, I suppose. In my viewpoint, its almost like restarting a file on a game and starting from scratch. Except everyone in that save file is going bat #@$% crazy because the end is near. Then you have those that don't even believe in the nonsense and are more worried over the Garleans invading, and go on with their merry little lives.

There was the Allagan Empire before the Garlean Empire, and there were probably even more before any of them as well. Astral is the beginning, Umbral is the end. Kinda like night and day, the sun and the moon, the light and the dark.

Astral is the light, the birth and energy to the world. Water, Earth, Wind. While Umbral is the destruction and the death in the world, Fire, Ice, Lightning. You catch my drift?

Most of these stories you can read more about from the books on the desks in the Arcanist Guild in Limsa, the desk in the Thaumaturges Guild in Ul'Dah, or the Conjurer's Guild in Gridania.

If you have anymore questions, be sure to ask. Hope that helped, and hope even more I wasn't wrong or too confusing!