I could see some human sacrifice - perhaps in imitation of the crucifixion of Christ? - just probably not to the same extent as the Aztecs who were themselves exceptional in the region.
And I think that the religion would still insist on a singular tripartite god, but with an incredibly strong worship of saints, spirits, angels, and "aspects of god" that are gods in all but name. And the Virgin Mary would still probably be predominant over the Santa Muerte at least in Mexico proper, though certainly associated as two sides of the same coin.
Possibly some Mormon missionaires had their message twisted, that Christ came to the Americas and is one in the same as the Feathered Serpent?
1. This probably works.
2. This pairs well with what I suggested earlier with saints joining a catholic pantheon and a "Royal Family" of the Gods in God/Yahweh, his consort on Earth the Virgin Mary, his Son Jesus and Jesus' consort Mary Magdalene.
3. Probably not? Maybe the Feathered Serpent has been canonized?
I think the states would be de facto and de jure independent. Those regions in the Precolumbian era were certainly independent of the Mexica, and in fact were constantly fighting them. They are probably minor hydraulic empires in and of themselves and have thus developed their own spins on Mexican Catholicism.
This is probably true. I'd say that earlier on, they were still de jure vassals but over time they broke away and really became Free and Sovereign States.
I would agree it maintains that name, though I think the sovereign would adopt the name emperor considering the name does have a very long history in Mexico and comes with implications of divine power.