Unfortunately, one of the very best sources that collects period accounts of these Afro-European mission encounters, if not the best, is almost entirely in Portuguese and Latin. If you have the language skills, that's Antonio Brásio, ed. and comp., Monumenta Missionaria Africana (11 vols., 1952-71), especially volumes 1 and 2 that cover the era up to the mid-16th-century. My Portuguese is bad, and my Latin is truly terrible, so I can't try to use those directly with anything like speed. Still, it's worth mentioning that they exist, as it's very useful in primary research if that's your topic and you have the toolkit.

The issue of when Diogo Cão took (and left) envoys, and why they went, is not entirely clear. The page you link is kind of devoid of referential clarity, but that may reflect real confusion. You provide 1485 as a return, which I've seen ascribed to Prince Kasuta's departure as an official envoy, to return with a third Cão's voyage in 1487. David Northrup, in Africa's Discovery of Europe (3rd ed., 2014 p. 20), characterizes the second 1484 interaction (1482 being first contact) quite differently: Cão landed four missionaries to make contact, and when ready to sail back, they had not returned, so he took four Kongolese as hostages (including Kasuta), though they became de facto ambassadors and educators in Kongolese language. Whether they came back in 1485 or 1487 is not clear; Cão reputedly died at sea in 1485 so couldn't make a third voyage as often ascribed. We only know that they definitely did return. Hans Debrunner's Presence and Prestige: Africans in Europe (1979, p. 42) puts Kasuta's trip to Europe as 1484-1485, with another in 1488-1490. Unfortunately, Debrunner doesn't tell us much about the content of 'education,' or about whether any of these early visitors converted or under what conditions, so it's still a bit unclear. But Kasuta was about as prominent a person as one could get, and had 'some success' per Debrunner in getting treaties and Portuguese skilled laborers to aid projects, so he clearly made a positive impression as a friend to Portuguese spiritual and earthly interests.

John Thornton has never placed proper exchanges that far back, instead pointing (in 1981) to 1493 as the first confirmed arrival of Kongolese for the purposes of education in Lisbon in his "Early Kongo-Portuguese Relations: A New Interpretation* (History in Africa vol. 8). So there's not exactly certainty or clarity there. It would seem to make little sense for many nobles to seek religious education as a goal before Nzinga aNkuwu's (João I's) conversion in 1491, although Jan Vansina (Kingdoms of the Savanna, 1966, p.45) states that many young men went to Portugal in 1487 specifically for schooling, along with a clansman of Nzinga aNkuwu's who was to represent the manikongo (king) and request more missionaries as well as carpenters and masons (This may have been Kasuta, but it's not clear from Vansina). They sent ivory and other valuables in quantity to assure their reception as people of means. That bit about the carpenters and masons is important, because it's part of the educational goal that doesn't quite reach fruition.

At the same time, there were many missions from Jolof and Bénin, so Kongo hardly stood alone; Northrup talks at length about them. Santo Eloi in Lisbon and São João in Xabregas were, according to Saunders and Saunders (Black Slaves and Freedmen in Portugal, 1441-1555, 1982, p.157), the usual places for informal and formal education in religious matters, under the auspices of the members of the Order of St. John the Evangelist. The starting date for the appearance of Kongolese at those institutions--1488--fits with the 1487 group. The content of this education is harder to describe, although discussions of the merits of Dom Henrique (the first Kongolese bishop, a prince born in 1495 and sent to Lisbon as a boy) take pains to mention his facility with Latin and theology as being at odds with his countrymen who had great difficulty mastering these subjects through a new medium at the time (writing). Of course, the Kongolese also wanted the technical elements of Portuguese culture, but religion--Catholic theology and orthdoxy--and language comprised the vast majority of education they received. The specific curriculum is not preserved anywhere that I've found, although this suggests that it conforms more or less to that given to Portuguese upper-class sons with, perhaps, more time on elements of writing and language, given the mention of those specifically in academic discussions. The discussions in Northrup and in others point to both a recognition of similarity of standing but also cultural difference, papered over in part by a common language of devotion to the Church or at least a seemingly sincere intent to take up the new faith. That was the case regardless of Nzinga's own hot-and-cold relationship with the Church, and it paid off in that sense when the Portuguese backed the succession of the deeply religious Afonso I in 1506-9. Inculcation of Kongolese nobles with the values [and skills] of Portuguese high society was a specific aim of this exchange, much as the importation of skilled Portuguese artisans was supposed to transfer skills to Kongolese, and translated early accounts speak highly of Kongolese as exotic but noble in bearing, with great cities and an organized polity that impressed travelers even into the disastrous 1600s.

The purpose of these educations is a bit clearer, and they also call back to the technical interests. To train Kongolese ambassadors and diplomats, educations in European social practices and languages were essential, including the language of religious faith. What's more, this regular traffic in young noblemen of Kongo--in good standing, as per Kongo's highly centralized state structure--meant that the Kongolese court had good knowledge of the Portuguese, their capabilities, and their relationships not too long after contact. In the volumes of documents (Brásio, above) are many letters from Kongo to the Vatican on ecclesiastical, spiritual, and more bluntly temporal matters, so connections directly to Rome began around the time of Dom Henrique's sojourn there at the start of the 16th century. There is no sign that they faced major social debility beyond that attending any new foreigner of stature.

So there was a decidedly functional reason for seeking the knowledge, because the Kongolese were aware that the Portuguese were not the only Europeans on the seas, and a succession of manikongos hoped to gain the technical knowledge needed to meet them on even ground materially and politically. They also had every expectation that they would be received as more or less befit their stature. Unfortunately, the Portuguese who visited--and the São Tomé planters, the Tomistas, who began demanding slaves--had much more interest in maintaining dependency, which is how the relationship soured so mightily later in the 16th century.

OP, I'm sorry not to have more fine grain about the specific interactions, but I suspect that any clear discussion or evidence is hiding in the primary sources that are in Latin and Portuguese. It's a great question indeed, because this was the same era that other Africans (including Ethiopians) were coming to Portugal and southern Europe generally. The visits of free people didn't decline in numbers until the 1600s, which corresponds to the massive upward tick of the export slave trades along the Atlantic generally.

[edit: Ecclesiastical has only three 'c's, not four; fixed some wording; clarified para 4]