Well here is my theory, although iI probably haven't though it out NEARLY as much as you guys:
All beings have their own magical energy. Most, however, do not know how to harness it. Around the time that Zeal was founded,someone discovered how to harness the Sunstone's energy. This person taught others (the Enlightened ones), although some people (Earthbound ones) just didn't get it. At some point , Lavos's energy was discovered, and as it was more powerful than that of the sunstone, the sunstone was abandoned and people started using Lavos energy instead. Sometime during all this, a very small number of people (Let's say 3. Let's also say the Gurus) learned how to actually harness their own energy. But, when they tried to teach others, they wouldn't listen, because Lavos energy was more powerful anyways, and all of the Enlightened ones, save maybe one *cough* Janus *cough* could harness it. I believe that Schala was just really really good at harnessing energy from sources other than (and possibly also) herself. The reason most of the people said that Janus seemed to posses no magical ability was simply because he couldn't harness Lavos's energy. If I recall correctly, the one Zealian who said that Janus had more power than Schala actually said that one of the gurus said that Janus had more power than Schala. And don't you think the gurus would be able to tell? Who knows, they may have even taught him some magic. Or Ozzie could've taught him, or hell, he may have figured it out himself. Anyways, I'm pretty sure that the during the fall of Zeal, everyone who could actually use their own magic was gated. And I'm also pretty sure that the sun stone also became unreachable. And they sure as hell couldn't go back to using Lavos, so the Enlightened ones couldn't use magic anymore, simply because all of the methods that they knew how to use had become impossible. And there was probably a lot of prejudice against those who figured out how to use their own magic afterwards, to the point where nobody who COULD use their own magic told anyone. Also, magical "techs" require no knowledge of magic and are used instinctively.
Thus when Spekkio teaches your group members magic, he simply teaches them how to harness their energy in whatever form he decides is appropriate. Thias is suggested by him saying "Well, you're a frog, so lete's give you water." He probably decided on Chrono's, Lucca's, and Marle's in a similar fashion. He didn't teach Robo because Robo isn't techjnically a living being, and therefore can't use magic. He didn't teach Ayla for one of two possible reasons: A.Giving someone from that early magic could potentially screw up the timeline a LOT. or B.He didn't think Ayla would be capable of understanding.
I also believe that the Elements are a way of harnessing the energy of the planet itself, much like with the sun stone, only with a more specifiic purpose for each one.