I think this is is a case of the "big thinks." How can you think to tie in Greek and Norse Mythology with chi? At some point, we have to deal more directly with the Chronoverse and what we know if it, and less with the real world (though real world parallels can provide insight, ascribing Serge's attack to "Chi" when "Chi" is never mentioned in the game itself doesn't make sense).
Again, I think I must help emphasize a line between CT Elements and CC Elements. There are four CT Elements. They are the balancing forces of the Chronoverse. These are, to me, the pure form of magic. You are truly using magic when you're using these elements.
The magical system of CC involves innate "colors." This is based on a Draconian understanding of the universe (quite sparated from Spekkio, THe God of War). The Draconian elements seem to be more geared to natural phenomena than the main forces of the universe.
The difference between a CT Element and a CC Element is like the difference between Gravity (a force in the universe) and an earthquake (a natural phenomena).
I don't really get a sense of duality with Shadow vs Heaven and Fire vs. Water. Shadow is somehow composed of the other three. A kind of primordial chaos.
Are there parallels? Sure. Magus uses Shadow and the character they intended to be Magus before dropping his storyline, Guile, uses the "Black" CC Element. Similarly, I think that indeed Crono would have been "White" instead of "Yellow" (though thats a matter of debate, I guess). Thematically, it makes more sense.
Crono's element is "Heaven", translated into "Lightning" here. His original magical attacks are consist of throwing lighting bolts (which, true to mythology, is a very heavenly association). He also has "Life" (ressurecting fallen allies, which is more of a game style element, in my opinion, because if any one of htem could have ressurected each other, why bother with the Time Egg to bring back Crono?) and Luminaire (sort of a "let there be light", big bang explosion).
In most ancient cosmologies, this connection makes perfect sense.
"Heaven" is not restricted to "lightning." Its a fundamental force of nature in the Chronoverse. Thus "heavenly" energy can be used to hurl lightning or to create explosions of light. Different physical manifestations of the same power (real world parallel: electricity can create lightning bolts, but also relates to electromagnetism).
The force "Heaven" governs a certain set of phenomena and can be used to create such. It would be interesting to see a more advanced magic user with the Heaven/Lightning element and all that they could possibly do. Something we can only ever guess at (unless they come out with Chrono Break and it has a lot more about this subject) is just how intricately the energies of the CT Elements can be combined and bent to one's will. The only real glimpse we ever get is Magus, whose use of Shadow is incredibly advanced. He's able to do a great many things (change Frog, somehow summon Lavos, etc) with his particular power, including manipulating the other elements.
Again, CC elements deal more directly with phenomena and less with the forces governing them. Creating lightning bolts, fire, bursts of light, water flows, etc. It doesn't take any special ability to use CC elements, contrary to CT Elements.