gotta love how an entire question is ignored because of a misconception that isn't even the focus of the thread. honestly, the question is just "WI Cortez was up to five years earlier/later than IOTL?" with what i posted before being just to give some context for why i posted this in the first place
But you did dedicate an opening paragraph to it. So you can't blame someone for pointing out the falsehood of a persistent myth of the Conquista.
How secure was Montezuma's position - as in, the security of him personally remaining in charge? I recall it being discussed that he wasn't exactly regarded as a great ruler even before this, but I might be mistaken.
I think his position was pretty secure. From what I read he made firm his predecessors conquests, particularly over the Zapotecs, continued the centralization efforts of the Triple Alliance overall, and dismantled many of the avenues that common born Aztecs could take to enter the nobility. Though the Calpulli - a sort of clan-guild structure, composed of both nobles and commoner family lines - were still the main source of social friction as they each controlled lands and held monopoly over trades, rather than the more traditional class conflict of other parts of the world. Given another generation or two, this hardening of class lines might have led to this development, but the 5 years proposed in the OP is probably not enough time to effect this potential direction much.
Outside competitors included the Tarascans who often allied with the Chichimeca groups to the north to counter Aztec influence; and down south, the empire was creeping its influence into the Guatemalan highlands. From what I read it's unlikely that this would have turned into military expansion anytime soon in either direction.
I read somewhere the Aztecs and Incas didn't know of each others existence. Is that true?
There were some traders from Incan lands known for going on long term voyages (the AH member Cuauhtemoc would know more, having told me about them). And their were reports from Spaniards of visiting Native merchants who wore very different clothing and spoke a different language that sailed along the Pacific coast of Oaxaca. If so, they probably knew very little about each other, and weren't very concerned being so far apart.
Would have had scant impact if any. Even if the Spanish are destroyed on La Noche Triste, there would be someone else coming over and the Aztec empire would have still alienated enough tribes to allow for alliances.
Cortes's expedition was one of several Spanish incursions into the mainland. All the others were complete disasters, and Cortes was a rogue agent. If he had failed, and then survived, he most likely would have been executed by the colonial authorities in the Caribbean. So there could have been a chance for the Triple Alliance to have adapted and put up a longer resistance, or other Mesoamerican polities to do so. It cost a lot of treasure and blood to launch these expeditions, and even the royal court wasn't too interested in them at first, wanting trade and conversion. The conquests just happen to pay off in the end. Also remember that the Spanish Empire was the result of more or less mercenary bands going about with their own funds to plunder and conquer. They frequently warred with each other, and could have been played off against each other by indigenous leaders if they had the time to realize how divided they were. OTL's turn of events are hardly guaranteed.