You gotta point with Lucca thinking a lot and the "short outs in her brain". Reminds me of a similar case in Earthbound where Brainshock, that causes strangeness (same as Chaos that may make them attack their teammates) where the higher IQ stat your player has, the harder it is to avoid. And naturally the genius (Jeff) would get it the most. In response to your observations:
Crono: I don't know what you mean by Crono being retarded. I mostly that he is a very well built swordsman who can be agile, and slowness would be opposite of that, so yeah, maybe that.
Ayla: Being affected by Chaos and Blind may have to do with her no nonsense "Just do it"(no Nike jokes please) personality.
Frog: He also has a kind of no nonsense personality, but poison... I really don't know. Aren't some frogs poisonous so it would be the opposite?
Magus: Not being affected too much makes since if he is supposed to be a master magician who can control several elements.
Robo and Marle: Well, Robo is a robot. and Marle, I just don't know. She's mostly a jack of all trades with resistance who is moderate to all. In fact, of the 20+ times I fought Lavos's Core, there was only 2 times where Spell actually did something to Marle (both Chaos)
As for Invading Light, Crono: pretty much every time, Marle: about half the time, Lucca: like never.
So there ya go for a thought exercise. I didn't pick my username randomly, after all.