[SPOILERS] Revelations from Patch 4.01

[Cilia]

While it's easy to assume that, due to Omega's near omnipotence, it is capable of dimension hopping and that's where it got the ideas for Halicarnassus and Exdeath from (literally from visiting V's world)... that remains unknown. According to Midgardsormr, it (like he) is "not of this star," meaning at the very least Omega is extraterrestrial. Whether or not it's extradimensional remains to be seen; until we know for sure it is, I would argue erring on the side of caution and going with what we know: that Halicarnassus and Exdeath are based on folktales on Hydaelyn, nothing more.

Omega states that its goal is to determine what allows us to overcome statistical disadvantages, then incorporate that into its evolution. As I argued before, this is likely a heart / soul, which is not something that can be obtained by simply desiring it or following protocol. It's a common theme with mechanical lifeforms: "What constitutes a soul? Can machines and other artificial lifeforms have souls?" The answer: often, but Omega is unlikely to grow one by following protocols to evolve. (Typically it requires going beyond mere programming, and again, despite Omega's near omnipotence all it's doing is following that programming.)

As for why we can't understand Alpha... well, we've never been able to understand beasts. That's Krile's shtick. More to the point and in regards to the whole soul business, I'd argue that Alpha presently lacks a soul for us to communicate with. He is, after all, nothing more than a cartoon chocobo created by Omega to lure us into its testing process. If we do gain the ability to speak with him using the Echo, that just proves Omega's creations can grow souls and move beyond their designated purpose. (Making Alpha the perfect counterpart to Omega: one weak and helpless, but possessing the one thing the nigh-omnipotent other cannot obtain.)

... mostly hypotheticals. Mostly. Sorry if I ruin the fun for everyone.