How come Tzekel-Kan didn't try to pass himself off as a god to the folks of El Dorado? He's charismatic, he's cunning, he's high versed in the study of the El Dorado religion, he certainly knows a lot more magic than Tulio and Miguel so he can actually pull off an example of divinity and not rely on luck, and he'd be able to pull off his insane "cleaning" project a lot easier. I'm sure the citizens themselves would probably think he's legit.
Because he's one of the locals. In every single case in history, every prophet, self-declared god or god's offspring had to leave his or her place of origin, because everyone there knew them and didn't believe them. It's like your neighbour suddenly declared himself a god. You wouldn't believe him, because you've known him for past x years and he was always just an average guy.
He's a (high) priest. Given the fact that he truly believes and awaits his gods, it would be blasphemous for him to self-declare godhood. Remember how he introduces himself as loyal servant. If not for that tiny cut on Miguel's eye brow, he wouldn't even dare to question our mighty and powerful duo. And going this way, he might consider Cortes his promised god.
How did the volcano not only stop erupting, but suck back in the volcanic air and die out? If a volcano is going to erupt, it's going to erupt no matter what. And of course, no one that was present for the volcano almost erupting before the 'miracle' occurred was a god/spirit/angel. So how did it stop?
Popular theory backed up by the original script is that the armadillo is actually the god and is the one responsible for the supernatural elements that help the heroes; note that the volcano stops erupting when the armadillo stops playing around. Not to mention during the ball game, the movements of the armadillo do not seem like those of a regular armadillo (the back and forth through the hoop without any assistance whatsoever). And since the gods created the game, it only makes sense that a god would be skilled at it...And then there's also the fact that when Tulio caught the fish, the armadillo looked ready to eat that fish whole. Normal armadillos eat bugs.
Where's the language barrier? The odds of the El Doradans encountering Spanish speakers, or really the speakers of any Indo-European language, before Miguel and Tulio are exceedingly slim. But it seems to be that the Spaniards and the El Doradans have no trouble understanding each other. Plus, that map that led Tulio and Miguel to El Dorado had to come from somewhere. Not to mention that the natives of El Dorado use an incredibly Spanish name for their own city.
To my memory, El Dorado is never referred to as such by the people living there—or by any other name, for that matter—so it could be called Tenochtihuacaxcalteccapicchusculuum or something for all we know. As for the language barrier...magic?
Actually, the chief says, "What a glorious day for El Dorado!" when Miguel says he will be staying with them. So it's definitely known as such to the citizens.
Maybe a previous explorer/lone conquistador did find the city through some impossible chance, befriended the inhabitants, and the people learned Spanish from them? And when they left, they were the one to make the map. So the lack of a language barrier could be the natives quietly switching to the Spanish they learned since their "gods" are using it.
Supporting evidence for "magic": Besides, well, how at least one of them does have real magic... in the scene outside of the waterfall at the "great big rock" they briefly communicate almost entirely non-verbally or else with Tulio trying to talk to the head soldier in a way that smacks of "I am trying to communicate (and probably failing at this)".
Say Miguel HAD stayed behind in El Dorado and Cortes had never found his way there. How would he explain how he was ageing like mortal human beings in the years he stayed thereafter? The chief is clearly aware that Miguel is human, but would the rest of the people be as understanding?
They could try to pass it off as something tied to his godhood, like "The gods are weakened if they stay in the mortal world for too long".
