Did conquistador freely admit their frequent and heavy-duty use of violence and other excesses? Yup. Did they face consequences for this? Usually not.

We do have quite some explicit descriptions of massacres etc. by conquistadors including Cortés. Since many of them were addressed to the Crown, usually the Spanish king would have known about this. Some letters were actually "best-sellers" at the time, because of the large interest in the events of the conquests. I would say that the main disapproval came only decades after the first conquests, with the Leyes Nuevas outlawing enslavement of native people. This was esp. connected to the Dominican Bartolomé de las Casas who strongly critiziced the mistreatment of the indigenous populations during and after the wars of conquest. Since you mention Cortés, let's have a look his example since it sums up some of these points pretty well.

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Cortés' letters are the only contemporaneous source we have on the Spanish-Aztec wars, with all others written after the events. Since he did not have royal permission to actually conquer anything in Mexico, Cortés' letters have to be understood at least partly as a justification of his actions before the Spanish Crown. This means many passages about attempts at christianisation (ostensibly the Spaniards main legitimation for coquests in the Americas) and about his own shrewd tactics. The letters also include many descriptions of the Spanish using scare tactics, as in many other parts of Latin America - including massacres of whole villages, meaning often women and children.

One instance of this is the infamous massacre at Cholula. It took place on the Spaniards' path to the Mexica capital, so before Spanish victory over the Aztecs. This massacre became well-known among other native communities, and can be interpreted as a use of strategic violence to showcase Spanish superiority. In his 2nd letter to the king, Cortés alleges that the Cholulans had conspired to kill him and his men, leading to these actions:

Judging from this information, as well as the signs that I had observed, I determined, to anticipate their movements, in order to prevent being taken by surprise; and sent for the nobles of the city, to whom I said that I wished to speak with them, and shut them in a room by themselves. In the mean time, I caused our people to be put under arms, and ordered them, when a gun was fired as a signal, to attack a crowd of Indians that had collected near my quarters, many of whom had entered within it. After I had shut up the nobles, l left them well secured, and mounting a horse, I caused the signal gun to be fired, and we made such execution that in two hours more than three thousand of the enemy perished.

The last sentence is jarring in its neutral description of the massacre of a city's population - explained by Cortés through an alleged Mexica-Cholulan plot that is hard today to (dis)prove. We have a few other, later accounts of the event. The first indigenous telling comes from Sahagún's Florentine Codex, book 12, set down in the second half of the 16th century. Despite the distance from the conquest, the Franciscan author's native interpreter's had close access to these events, since they talked to native elders with better knowledge of these. According to the Florentine Codex:

When the Spaniards heard this, they went to Cholula, taking those of Tlaxcalla and Cempoalla with them dressed for war. When they arrived, they shouted for all noblemen, rulers, captains, chiefs, and also the men of the town to assemble in the courtyard of the gods [probably of the Temple of Quetzacoatl]. When they had all gathered, [the Spaniards and their allies] blocked the entrances, all of the places where one could enter. In the first moment, people were murdered and beaten. Nothing like this was in the minds of the Cholulans. Without swords or shields they met the Spaniards. Without warning, they were treacherously and deceitfully slain. They were ambushed because the Tlaxcalans persuaded [the Spaniards] to do it.

And everything that had happened, everything that had taken place was told, was relayed to Moctezuma. Some of the messengers came, while others left; they turned around and took flight. There was no time when they did not listen, when there were no reports. For all of the common people were filled with fright. There were frequent disturbances. It was as if the earth moved, as if the earth quaked, as if everything was spinning before ones' eyes. There was wonder.

This later account by the Tlatelolca scribes is quite different in that here: the Spaniards very purposefully gather the unarmed Cholula elite, and then kill them in a surprise attack. The impetus is here given by the Tlaxcaltecs, then the Spaniards' main native allies. Both Spanish and Tlaxcaltels would have had enough motivation to contuct such a surprise massacre, although it's difficult to completely discount if there might have been some plan on the Cholulan's side. Either way the massacre served the purpose of setting fear into the adversaries of the Spanish, as shown in the last sentences of the quote. My main point being here that Cortés did not shy away from describing what was clearly a massacre directly to the Spanish Crown - this only one of many examples. (both accounts I mentioned can be read in more detail on this AHA page - Cortés here and Florentine Codex here)

Pizarro, the main conqueror of the Incan empire in the Andes, did/could not write. But we do have accounts of other soldiers and priests taking part in his campaign, who describe some similiar tactics - e.g. massacres as a strategy, and the early capture of the Incan ruler Atahualpa, similiar to Moctezuma's capture through Cortés. Again, there was no censure of Pizarro as long as his plans fit with the Crown's intentions. It has also been highlighted in this context that the conquistador's emulated the medieval Iberian "reconquista" - they also imitated the romances that retold the campaigns of the Iberian Christian states against the Iberian Muslim states as fights against "infidels". Here (and in many other forms) the Iberian Muslims were compared to the American Indians, and the fight recast as one against infidels who had to be converted. This at least partly explains why the descriptions of brutal conquest in the Americas would have not come as a such a surprise to Spaniards in Europe.

In the end, Cortés did not get reprimanded but actually received a huge encomienda in Mexico in return for his actions - making him marqués de la Valle (in modern-day Oaxaca). He had travelled to Spain to secure these rights. Overall, I would say that pressure esp. by de las Casas led to a slightly better situation for the native people with the Leyes Nuevas. They could no longer be enslaved officially after 1542, but the working conditions only improved slightly and quite temporarily. All this had also to do with Crown interests - after all after most native people had died or been killed in the Carribbean, this was not economically viable for other parts of the Americas (excuse my economic language here, meant to emulate Spanish ideas of the time).

The actual pushback by the Spanish Crown against conquistadors would only come after the Leyes Nuevas. This was a) because esp. in Peru and Mexico, conquistador elites feared loss of power through the Leyes Nuevas, leading in some parts to rebellion, and b) because the Crown increasingly tried to limit the conquistador's influence because of fears that an American nobility would form. The initial critique of mistreatment of native people then came from esp. religious orders like the Dominicans and Franciscans, who would later influence Crown policies in some ways.

columbus, when speaking of first contact with arawak tribes writes, "...they do not bear arms, and do not know them... they have no iron. they would make fine servants... with fifty men we could subjugate them all and make them do whatever we want." he later writes that he immediately took prisoners by force for information about gold deposits and other sources of wealth in the area. after island hopping through the caribbean, taking more prisoners and murdering a few arawaks for not trading as many bows and arrows as he and his men wanted he headed back to spain. his exaggerated claims of bountiful gold and riches brought about a second expedition with 1200 men for the explicit purpose of capturing slaves and taking gold. his justification was religious, saying "our lord, gives victory to those who follow his way over apparent impossibilities," and "let us in the name of the holy trinity go on sending all the slaves that can be sold."

Thus began the european invasion of the americas. when gold was not found in quantities promised by columbus to the crown he instituted impossible directives, punishable by death, leading directly to the murder and mass suicides of half the island of hatis native population in two years. when the hunt for gold was finally slowed, mass enslavement began. by 1650 there were no more natives left on the island.

bartolome de las casas, a priest, is the main source of information on treatment of natives on the islands after columbus arrived. originally a part of cubas conquest, he became a critic of spanish violence against natives. he writes the spanish "grew more conceited every day" and that the natives "mild and pacific temperament" was met by the spaniards desire to "exasperate, kill, mangle, and destroy... the admiral, it is true, was blind as those who came after him, and he was so anxious to please the king that he committed irreparable crimes against the indians.." la casas did not stop the cruelty perpetrated against the indians, but his published works on the treatment of natives did however lead to towards some reform.

the cruel policies put in place by the conquistadors were not, in fact, always backed by the crown. King Carlos I of Spain issued an edict in 1542 banning the enslavement of natives but this had little effect on the frontier. as an example, in 1546, 15 colonists in the yucatan were killed by the maya. retaliation by the spaniards was brutal, with the enslavement of 2,000 men, the hanging of their women, and the burning of six native priests. this "bloody slaughter and destruction" of natives was technically illegal but, as is seen time and again during this era, spanish laws protecting natives were rarely enforced. the crown depended upon money and slaves from the new world to finance wars in europe and allowed for some defiance of crown law.

money and power hungry, conquistadors themselves were eager to create for themselves a new ruling class in politics, one that at times simultaneously defied the kings orders while claiming to fight for spain and the king in the new world. after several edicts and laws were passed to limit the power of conquistadors in the new and old worlds a demand was made. calling king phillip "nothing but cruel and ungrateful" in a letter to him, lope de aguirre says, "I demand of you, King, that you do justice and right by the good vassals you have in this land, even though I and my companions (whose names I will give later), unable to suffer further the cruelties of your judges, viceroy, and governors, have resolved to obey you no longer. Denaturalizing ourselves from our land, Spain, we make the cruelest war against you that our power can sustain and endure. Believe, King and lord, we have done this because we can no longer tolerate the great oppression and unjust punishments of your ministers who, to make places for their sons and dependents, have usurped and robbed our fame, life, and honor. It is a pity, King, the bad treatment you have given us.."

gotta go ill finish later probably

We prepfere the term central america rather than middle. Also hernan cortez technically Conquered part of North America.

As to your question according to what Bernal Díaz del Castillo, reported in his Historia Verdadera de la conquista de la nNueva España (something alog The True story about the conquest of the New Spain) he recall that most of their acts were not very honorable. although their real mission was to spread the power of the spanish crown. And also he writtes abourt how he as one of Cortezes men turned against Pedro de Alvarado when the Governor of Cuba sent a punitive expedition against them. according to him this was done out of pure greed and desire for power.

Sorry about any issues in my English