A vast amount of the population seems to have native and spanish ancestry (including myself) some people even of other european ancestry and what i'm really curious about is: was it common for spanish settlers to marry native women or men? Did this happen mostly through rape? Maybe extramarital affairs? If any of this is correct why did this happen?
Also I'm open to the possibility that the premise is incorrect in which case i would like to know why most of us have European last names but don't look like it. Thanks for reading the really long question
It was indeed common to marry indigenous women, and also to be in couple with them despite not being married (amancebamiento). As to why it happened, there a number of factors.
First of all, the first explorations were carried out by men: sailors, soldiers, military officers, and friars. They were military expeditions, more often than not, so it would be awfully hard to find women amongst those expeditions. When Hernán Cortés journeyed into Mexican territory, he only had a few hundred men, not a few hundred people, we are talking soldiers and officers. Malintzin, Hernán Cortés' interpreter and later his lover, was the exception. Those soldiers and officers would be men without women, and who had one thing in mind: to carve fiefdoms for themselves and rule those lands as lords.
For this point to succeed, there were two ways: being granted a lordship for the services rendered to the Crown, and getting the fiefdom first. The first way is pretty straightforward, the second would normally require to marry into the indigenous aristocracy, which would give them rights to the lands, and would also make the control of the territory much easier, as the new rulers would be more easily accepted by the vassals, as those rulers were of their own kind. Some examples of these marriages are the daughter of Moctezuma being married to a number of Cortés' own captains, or the descendants of the aristocracy who rose to prominence like the Inca Garcilaso (descendant of the Incas), or Fernando de Alva Ixtlilxochitl (descendant of the rulers of Texcoco).
This submission through marriage to the local nobility made control of the territories much easier, as control through military might alone was extremely hard to exercise due to the enormous numerical superiority the natives had against the Spanish. When the epidemics like flu, measles, smallpox, etc started ravaging America, the Spanish and their descendants were much more likely to survive, and this included the ones that had married and had offspring with th the native populations, resulting in a higher percentage of mixed race people due to the natives dying of the plagues.
These marriages and unions were not only looked upon by the Crown, but were welcome for the reasons explained, which resulted in ordinances and laws permitting the marriages, and even promoting them. In 1514, both Rodrigo de Alburquerque and Gonzalo Fernández de Oviedo promoted these unions in order to get more settlers.
Local aristocracies, when converted to christianity, were integrated into the power structures, which also resulted in them marrying into the Spanish nobility, cementing the Spanish power, and strengthening the ties to Spain. Spain recognising these aristocracies resulted in some rather unique institutions, like the Alferazgo Real de los Incas in Lima, more or less protocolary but worth mentioning. These alferazgo was composed of the descendants of the twelve panacas, the families of the former Sapa Incas.
Sources:
Encinas, Diego de (1586), "Cedulario Indiano". Madrid: Imprenta Real.
Fernández de Oviedo, Gonzalo (1535), "Historia General y Natural de las Indias". Seville, Cromberger.
Thomas, Hugh (2010), "The Spanish Empire of Charles V". London: Allen Lane.
De la Vega, Inca Garcilaso (1609), "Comentarios Reales de los Incas". Lisbon: Pedro Crasbeeck.
You already received a fine answer by /u/tywindevillena; in addition you may be interested in my answers on related topics, mostly for Mexico:
here on intermarriage between Spaniards and indigenous people in colonial Mexico. I should add that Spaniards only ever made up a small percentage of the American populace during colonial times, with the majority being indigenous. And that while tactical intermarriage between elites happened as I described in that post, mixing was due more to rape and forced marriages in the conquest and early colonial periods; and to illicit relationships (concubinage) during the colonial middle.
here on immigration of Spanish women - another important factor because few European women migrated until the later 16th c.
Here more specifically on descendants of Moctezuma II.
Hope this helps!