​ Hey! I've written quite a bit in connection with this topic: You may be interested in the relevant sections in my profile, and my reading recommendations.

Of course you're asking about processes taking place overa long time-frame and a huge region. To put it very briefly: Indigenous culture and socio-political forms persisted in different ways througout colonial times, especially in more rural regions. However, especially in the cities gradual Hispanic influence had spread in many areas at least by the mid-to late 16th century. James Lockhart has argued that by ca. the 17th century a stronger Spanish influence is evident in native languages and other areas. At the same time the oftentimes forced conversion of native population led rather to a "native Christianity" that also retained many elements of pre-Hispanic religion. We can overall note a stronger Spanish influence in certain regions (esp. central Mexico) and areas (incl. religion and administration) that was, however, built on indigenous structures which continued to exert influence as well - so not a simple replacement of native by European culture/society.

Some of my answers that are more specifically on such questions:

• Why did the "Spanish" conquest of Mexico end up that way? That is, why did Spain end up with dominance over the former Aztec territories, instead of Tlaxcala or the other native allies who far outnumbered the conquistadors? (on political and administrative organisation)

• How did the descendants of Montezuma II become Spanish nobility? (on native nobility)

• Are native Mexicans considered an indigenous people ? (Including parts on the casta system & indigenismo)

• An answer from an AMA dealing with religious education of native elites

• Foreign and Local Origins of 19th Century Mexican Land Reform

Hope this helps - If you have any more specific question let me know.