I'm sue we're all familiar with the stories of the conquest of the Aztecs and the Incas, and how small Spanish forces were able to defeat vastly superior numbers of native forces due to technological edges, most notably cavalry, guns, and steel armor and weapons. I'm quite aware by now that the vast bulk of Cortes' army was actually native allies, but what about Pizarro? Did he have a similar situation? How were the Spanish able to hold onto Peru despite the disparity in numbers, being far away from friendly territory, and protracted resistance? Was the technological gap just that great?
Hey, these are some big questions, and I can only provide some answers for Mexico/New Spain and not Peru. Just a note to your text: in all Spanish conquests at the time both indigenous allies, conflicts between native groups, and diseases played major roles in Spanish victories, arguably more so than any technological advantages. For a good & very readable overview over the Spanish military campaigns I'd recommend Restall's Seven Myths of the Spanish Conquest.
For the early post-conquest period:
I've written a bit on Spanish colonisation of Mexico before, some of which is on my profile
Another answer of mine is spefically on indigenous resistance to Spanish rule there, immediately after conquest
And this one talks about Spanish influence on politics and organisation (heads up it's longer)
As a quick note: usually it's mentioned that there were many parallels between the conquest campaigns against the Aztecs and Inca. E.g. in both cases major conflicts between different native groups/ruling factions; and the Spanish building on their pre-existing political structures, which led to these regions actually forming the first power centres of the Spanish in the Americas. However, we have to be careful not to cast both cases as too similar - e.g. the native elites in the Andes probably managed to hold onto more power than their Mexican counterparts.
Hope this helps!