part 1
This is a huge area and topic, where experiences would vary accordingly - I'll focus mostly on central Mexico as per usual, although there are many parallels with other parts of Spanish America. Overall, the easy answer would be that of course, there was not only one experience of or response to conquest and diseases and slavery.
There were many responses, ranging from lamenting the dead, to the need to record one's ancestors' possessions and histories in the face of tragic population loss. But despite the demographic catastrophes, indigenous cultures continued to adapt and survive until today - far from supposedly "giving up" or showing despondency, as many European colonial writers would have it.
Traditionally, most history writing on the conquest campaigns and colonial period in the Americas has drawn on European sources. Often Spanish writers would describe the conquest as “zero hour” and a major event in human history. For conquistadors this made sense in order to glorify their own deeds; for members of this clergy this could underline their self-appointed mission of converting the native population to Christianity. Especially conquistadors (like Cortés in Mexico) helped also to create a narrative of supposed “native despondency”: this meant that native Americans were supposedly so overwhelmed by first the Spanish forces and then by colonisation that they would often respond passively or sort of give up.
At least for colonial Mexico but also many other regions, the last 30 or so years have led to a big inrease of great works drawing on all kinds of indigenous sources – written, glyphs, maps, quipu (textiles) among others. One consequence of this has been to challenge more traditional views of the conquest as those sketched above. Just to mention a few, Matthew Restall has countered what he calls this “myth of native despondency”. For him, native Americans actually responded very actively and intelligently to the Spanish intruders. In places including Mexico and Peru, indigenous groups or factions would form alliances with (and sometimes against) the Spaniards in order to improve their own situations. He counters claims of the natives' supposed fear of European weapons – native were actually very quick to take up and adapt weapons including swords and fireweapons from the start.
Moving beyond the conquest period, we can see continuities with the pre-Hispanic period as well as adapting of European culture in all domains. In central Mexico, native intellectuals and communities were taught Latin alphabet in order to aid in their conversion. This was then used in a variety of major projects that have actually helped to pass on pre-hispanic history and traditions until today. Native languages and beliefs were changed, certainly, but have also continued to stay in use in various forms – e.g. with “imperial” languages like Quechua and Nahuatl made more important than before though the religious orders' efforts, while others languages were more marginalized. And with elements of native beliefs often surviving through the creation of a mixed “native Christianity” (all these are huge topics of research, so simplifying a bit here).
Importantly, such a focus on continuities should not in any way downplay the major and catastrophic effects of colonialism, diseases etc. on native populations across the Americas (and elsewhere). In parts of New Spain/colonial Mexico alone, mortality rates from the many diseases that hit the indigenous populace until the early 17th c. could go up to 90%. These were then compounded early on by slavery; and when native slavery was abolished in the mid to later 16th century, native people continued to suffer harsh working conditions under the encomienda and then the repartimiento work systems. In addition, at the turn of the 17th century in different regions of Spanish America a reorganisation of communities took place. Through this, large numbers of people left their traditional lands, or where forced to seek work elsewhere. At the same time, the huge population loss meant that many nearly empty villages where “taken over” by Spaniards and other groups.
All these, and esp. the demographic catastrophe were noted and lamented by native authors. Of course, since most writings that have survived (at least again for central Mexico) come from members of the native elites, their focus could also include the loss of political and cultural influence after colonisation. But many writings and paintings by communities were also made, often collectively, that reflect upon the losses suffered – both in community members, and in properties and traditional lands. This is to say, that focusing on the existing continuities from pre-hispanic to colonial times should not mean to relativize the very real suffering and loss of people and traditions that conquest and colonisation meant. So that while the Spanish conquest is usually perceived as one among others, the direct, often devastating effects of colonial rule and reorganisation are very much chronicled, and in many cases proved more consequential than the conquest itself.
Going back to the initial Spanish claims of a “zero hour” – interesting studies like those of Stephanie Wood have argued that in central Mexico the Spanish conquest was not seen as a major event at all. Rather indigenous chroniclers would simply see it as one more in a long line of conquests in Mesoamerica. Wood (in “Transcending the Conquest”) discusses among others pictorial sources, where the Spanish are not portrayed as particularly special or menacing; they are just another group, albeit with a different skin color. For her. Such sources do not reflect a “radical difference” of the Spaniards and their practices from the indigenous POV. Rather Spanish modes of though and structures are integrated into Mesoamerican ones. This, again, goes counter to claims of Spaniards who of course had very different interests in portraying these events as major cataclysms of change.
Some writers like annalist Domingo de Chimalpahin (writing in the early 17th c.) would even see the Spanish conquest of his ancestors, the Chalca, as a much less distruptive event than their earlier conquest through the Aztecs. After all, the Aztecs for a few decades removed the ruling dynasties from power, while under the Spanish these Chalca families could hold onto their rule for some time. This perspective again points to larger trends: At least until the mid- to late- 16th century, in many parts of central Mexico native elites held their posts of influence and possessions, although their influence would usually decrease afterwards.
To some this up, an increasing inclusion of native perspectives has then shifted the focus towards indigenous agency, and continuities with pre-hispanic structures and traditions. This helps to also overcome earlier studies that have focused on a supposed “incomparability” of the Americas or possible “acculturation” of native people. Lisa Sousa sums some of this up well (in “The Woman Who Turned Into a Jaguar”):
[b]y focusing on mechanisms of indigenous production and the work of native women [and more generally native people] ..., we decenter the traditional focus on the North Atlantic and Europe, [and] challenge historical narratives of western progress and the civilizing influences of colonialism.