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 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.
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.