Do you get a Holy Grail if you win the game the Beings play?

The Game has no known concept of “winning.”

Are there any notable historical figures who had their own Beings?

Oh, probably.

What supernatural tales were inspired by the existence of Beings? Walking on water? Moving mountains?

Several popular anime.

Evangelion’s Angels ate from the Tree of Life, thus going on different evolutionary pathways than humans despite a common ancestor. Mushi are the first stage of life that emerge from the River of Light, predating even bacteria. How do Beings fit into the overall ecological structure of the planet? Are they part of the normal organism kingdom system we use? Or, like the Angels and Mushi, do they represent something that exists outside our understanding of how life emerges and evolves?

Well, now, that would be telling.

Does the military use Beings, and if so, in what capacity?

Some have tried. However, for various reasons it’s not a convenient strategy.