I'm no Hispanist, but I do have experience with the literature of the conquest of the Americas in English and Spanish and I might be able to point you in the direction of a few resources and scholarly works. (I can't comment on Portugal, unfortunately.) Below, I'll respond to your questions in sequence:

Did the Spanish and Portuguese keep any records on the various native groups that they subjugated?

Yes, the Spanish kept extensive records on the native inhabitants of the Americas. Much of this literature is stored in the Archivo General de Indias, an immeasurably valuable resource for primary texts written in the colonies. (Many of the works are now digitized and can be accessed online.)

did the Spanish/Portuguese governments in Europe know which native cultures ... were present in the new world and how they came under Spanish/Portuguese rule, as well as what their society and governance was like before their conquest?

Spanish historiography on the colonization of the Americas and on Amerindian societies, both pre- and post-Columbian, is monumental when compared to the English writing. While the Spanish had such figures as Pietro Martire d'Anghiera, Gonzalo Fernández de Oviedo, Bartolomé de las Casas, Antonio de Herrera y Tordesillas, Antonio de Solís, among many illustrious others, the English colonies first comparable work is Robert Beverley's History of the Present State of Virginia (1705). Part of the reason for the disparity is that many of the famous Spanish historians were official chroniclers for the Spanish state, a position that did not exist in England.

Information about the unfolding conquest was transmitted in official reports back to Iberia, such as Hernan Cortés's Cartas de relación. The genre of the relación, also exemplified in Álvar Núñez Cabeza de Vaca's Naufragios, was a legal representation of services rendered, full title for which was relación de servicios.

The second voyage of Columbus carried four friars to the Americas who were tasked with evangelizing to the Amerindians. The first mission to Hispaniola led to the earliest ethnographic study of indigenous religion in the New World, Ramón Pané’s Relación acerca de las antigüedades de los indios (1498), an important source for Martire's account of Spanish colonization.

If so, how did they get this information, of what quality was it, and to what extent was that information used in setting up the administration of the Viceroyalities and colonies?

Bernardino de Sahagún's work, known as the Florentine Codex, is an example of how pre-Columbian history was transmitted to Spain from the colonies. The story is complicated by the fact that Sahagún's work fell out of favor. Nonetheless, like a number of Franciscans, Sahagún interviewed Mexica scholars who interpreted for him the amoxtli, pictographic texts that were supplemented through a memorized oral tradition. The study of indigenous culture, especially religion, was considered a way to develop better evangelism and to recognized heretical spiritual practices. Because much of the information was self-reported by indigenous scholars, the information does contain a lot of value, though its historical accuracy is hard to gauge.

Actual Amerindian writing, such as the Mendoza Codex, made its way across the Atlantic as well.

That's all the time I have to respond for today. I hope this was somewhat helpful.

Yes, there are records, but the process of conquest shaped what information they contain.

The Spanish conquest was not a state organized military endeavor. It was privately financed, organized, and led. Conquistadors asked for royal permission, but the monarchy did not finance them. Consequently, most early written records are by conquistadors who sought to impress the king with their exploits in order to gain more favor, rewards, and benefits after the conquest. In some cases, this meant exaggerating native resistance, or negative aspects of native culture, barbarism, cannibalism, etc. At other times this meant ignoring, or downplaying, the huge role played by native allies. For example at the siege of Tenochtitlan, Cortes' Spanish forces were outnumbered many times over by their native allies. Yet, his letters do a poor job of describing their contribution.

The other salient fact, is that, alongside conquistadors, missionaries frequently wrote to the king in their efforts to promote Christianization and to combat what they saw as excesses by conquistadors. In these records we also see descriptions of native civilization and culture. Yet, like conquistadors, missionaries also had their own goals. They wanted to promote the need for their efforts so they could at times exaggerate the heretical beliefs of natives or exaggerate idolatry and pagan worship.

Did the accounts of conquistadors and missionaries shape policy, yes they did. In Spanish America, they led the king to establish laws protecting the natives from abuse by secular Spaniards, but also entrenched racial stigmas and discrimination into the legal system. Based on the reports of both missionaries and conquistadors, natives were thought to be in need of protection because they were too simple, too childlike, too irrational to be full equal subjects of the king.

The location of viceroyalties was determined precisely because of the human geography of Native Americans. The Viceroyalty of New Spain (Mexico) and that of Peru were created on the political structures of the Aztec and Inca Empires. The Spanish conquest did not so much destroy those empires as co-opt and take over their structures.

The most directed effort at gathering this type of information was made in the late sixteenth century when Phillip II of Spain ordered that every community (especially indigenous ones) fill out and return a questionnaire concerning various topics of governance, economy, society, territory, etc. These Relaciones Geograficas are an amazing set of cultural data concerning many ethnic groups within the Spanish Empire. Another mid-sixteenth century compendium of indigenous culture is that of the Franciscan friar Fray Bernardino de Sahagun known as the Florentine Codex a document he called the Historia Universal de las cosas de la Nueva Espana This encyclopedic volume contains information about the mythology/religion of Aztecs, the history of the Aztecs, information about medicine, native plant and animal species, and an indigenous account of the conquest.