1. I meant the Inca more than the Aztec for learning from the conflict. The latter had the issue of believing that the world would die if they didn't feed the gods every human heart they could, obviously discouraging tactical innovation. This was simply not a factor for the Inca. However I said both because I do not think it completely impossible for the Aztecs to learn.
2. Without Cortez I find it very unlikely that the Spanish forces manage to survive in anything other than ragged clumps making it back to the coast, whose stories would be quickly discredited more likely than not IMO. Furthermore I think it likely that one or more of the small groups of survivors treats the Natives rather terribly, discouraging them from the whole alliance thing.
3. Yes, but they think that the entire continent is filled with gold whilst one particular corner of it is filled with savages who can wipe out small armies of Spaniards. Thus the Spanish go elsewhere looking for gold, but consistently come back empty handed. Ultimately Mexico becomes a second Florida in a sense, but its unrealized value lies in gold rather than good agricultural land.
Alternatively, maybe the Conquistadores
do conquer the Aztec. The question remains, can they hold it if the King explicitly refuses to lend any veneer of legitimacy to the colony and its simply rule by the strong? That's not a recipe for internal stability, and we know that the Spaniards will have to deal with revolts eventually further complicating matters.
Which brings me to 4. The King has a very strong interest in not allowing territories beyond his control. Why should he accept a little bit of gold now when he could get all of it, as well as a much more permanent power in the Americas, by waiting (what he thinks) is a couple of years, before of course things get out of hand (cf. Martin Luther)? Why should he take the risk of letting any man's word in the colonies acquiring more strength than his? Power and prestige are important in addition to gold, you know.
5. The first colony in Panama was founded in 1519 and by the early 1520s transisthmian roads were being constructed, well before the conquest of the Inca was any sure thing (particularly if you accept that ITTL the boldest of the Conquistadores will be in Mexico). This, in turn, suggests that a greater focus was initially thought to lie in the transpacific trade, rather than in stripping the Andes of resources. Thus Drake would still be sailing up the Peruvian coast to get to Panama and cross the Pacific from there along the Galleon trade routes and would likely make contact with the Inca at some point. Now, I do not dispute that Drake was perfectly capable of perfidy when the situation called for it. If anything, his first contact with the Natives in the Andes would be by kidnapping. But at the same time, I doubt that he or the English generally would refuse to trade with the Inca once it became obvious to them that, due to lack of a suitable base, they had no real hope of conquering them.
Down the road, I could see something like the following playing out:
1. Virginia is founded in OTL Argentina, with Jamestown at OTL Buenos Aires, with the Virginia co. thinking that they'll be able to find the same gold that the Inca are getting. Ports are established in OTL Chile to facilitate trade.
2. They realise that, due to the Atacama desert, it would still be rather hard to conquer the Inca, and trade begins with the English selling guns and food in exchange for gold.
3. Inca become something like a South American Iroquois, but have a much more defensible position. The Iroquois show that even a native group with extremely unreliable access to firearms can still be a major player, and I think that the Inca would figure out metallurgy much faster than the Iroquois did. Furthermore they have much more access to natural resources.
4. For a while the Inca serve as a buffer state between English and Spanish territory. Neither side really wants to provoke a war over it. Eventually someone might conquer them esp. in TTL independence movement but it's very hard to predict so long after POD.
This scenario essentially requires the Inca to survive ~80 years longer than IOTL. IMO, this is not a hard proposal. Remember that even IOTL, it took the Spanish almost fifty years to conquer Peru entirely, and they had a massive advantage in that they showed up just as a civil war was starting.
Assuming, as you insist, that Mexico is still conquered fairly soon after Cortez is killed, which I doubt for the above reasons, I would imagine that it takes the Spanish at least another 5 years to organise a new expedition and conquer the Aztec and 10 years, possibly closer to 20, to pacify the territory to the point where there are enough conquistadores who want to fight for Peruvian gold rather than Mexican Encomiendas that an expedition into Peru starts entering the cards. Without an ongoing plague and civil war, the Sapa Inca can crush the first arrivals at least four times out of five. Furthermore the Inca, unlike the Aztecs, have no religious reason not to adapt to Spanish warfare, and even if they don't adopt firearms the use of crossbows (bullets are easy to figure out relative to powder) and metal weapons and armor by the "King's guard" massively change the picture, as does the fact that the Inca can now prepare to counter the kind of warfare they will face (esp. basic anticav tactics). Thus, the Inca can consistently rebuff small Conquistador expeditions, building up their inventories of metal weapons/armor each time. The very system of conquistadoring that enabled low-cost expeditions to take out the two empires IOTL now plays against the conquistadores, none of whom want to wait until enough people have gathered for a full-scale army. Thus, the Inca can IMO
easily last until the early 1620s for trade with England to come into play.