I agree that the citation from Kellner seems to point to not simply premodern (i.e. before 1800) peoples but actually prehistoric peoples. To confirm this, of course, you would want to actually look up the passage from which the author quotes. The whole question of how people historically understood their own identity is pretty complex. In the Middle Ages, this question has often been dominated by a debate over whether, and when, the Middle Ages even understood people as individuals in the way we do today. Several of your follow up questions would require whole books to answer! This is not my area of specialty, although I am a historian of medieval Europe. That said, some basic information about medieval society may help you.

I presume the question "would this even be true..." refers to the author's assertion that people "did not experience identity crises or modify their identities..." I'm not sure how much evidence we have about those specific issues and would have to defer to someone with more specialist knowledge. However, it is fair to say that in the European Middle Ages people primarily understood themselves in terms of their social status and family, things that did not change much. If you were a man born into a serf family, you would be a member of that family and a serf of that lord all your life, and would expect at some point to be a husband and father. If you were a man born into a family of craftspeople, you would almost certainly take up the same craft as your father. Men from noble families thought of themselves primarily as members of that family, and secondarily in terms of loyalty to a particular ruler.

Two major exceptions to this pattern in Europe were the Church and women. By definition, you could not be born into the priesthood or a monk or nun, so these statuses were acquired sometime in, usually early, adulthood. Although most men and women who became priests, monks, and nuns were people from land-owning classes, there were exceptions and sometimes those from more humble backgrounds were able to join the ranks and improve their station somewhat. Women, the second major exception, usually married and effectively became members of a new family, acquiring a new identity. However, women as marriage partners were usually valued according to the desirability and wealth of their families, so often they had a sort of dual identity: both as members of the husband's family and the family of origin. So with those two major exceptions, women and the Church, people were born into categories of family and social status that remained fixed.

In answer to your second question, it's probably not even helpful to thing of such a thing as "jobs" in the Middle Ages. There were a relatively small number of people then who depended for their livelihood on performing waged labor for an employer, and for the most part those people were of the lowest status in society. Most people were agricultural laborers who for various reasons were not free to simply do something else just because they felt like it. A smaller number were landholders who lived off rents and crops, but had to perform certain duties as a condition of holding those lands. Another group were craftspeople who learned a trade from late childhood onward. Before modern machinery, learning a craft took many years, and the tools and equipment needed to perform it were major investments. Apprentices were children by definition, so once you apprenticed into a trade, it really wasn't a viable option to decide you wanted to do something different and become an apprentice again. Choices made (often by someone else) in late childhood were lifelong. In the later Middle Ages, this was increasingly less true and starting from the 1200s onward, new religious options (like the Franciscan and Dominican orders and their confraternities for lay people) opened up that people sometimes took advantage of and made major life changes in adulthood.

Moving on to your other questions, it is important to understand that there was no such thing as a "teen" in medieval Europe. Thus, a lot of things that we would associate with that just didn't exist in any similar form. Also, since there was nothing really akin to modern popular culture in the European Middle Ages, there was nothing really very similar to "fandoms." There were a few historically recorded crazes or fads that caught up children or persons we might now consider teenagers or young adults, like the Children's Crusade. Young male apprentices had their own social life distinct from that of other people, with their own kinds of initiation rituals and celebrations. In some places, like Italian city-states, there was something not unlike a gang culture among young men of middling status. For the most part, unmarried young women were kept under strict surveillance by their families because of the high premium on virginity and the danger not simply of sexual indiscretion but actual kidnapping and/or rape. Therefore, girls and young women didn't have many opportunities to socialize in groups and develop their own distinctive social life in the way many boys did.

Everything I have said here is a generality, and there were exceptions. But in general, premodern societies, including that of the Middle Ages, did not place a high premium on individual self-expression or autonomy. Medieval society generally rewarded those who understood the status into which they had been born and fulfilled the obligations and expectations attached to that status. It generally did not reward or approve of those who desired to forge for themselves an identity of their own choosing, without reference to the ties of family and class into which they were born. This starts to change a little around the fifteenth century, in an elite cultural movement called the Renaissance. But it took a long time (centuries) for new ideas that valued the individual above society or family to really take hold more generally.

I'm not sure what sort of further reading would be most useful for you. A lot of what I've said is actually fairly well illustrated by the Showtime TV series The Borgias, which is set in the very early 1500s. One very interesting book about a law case in the 1500s concerning identity, which was also made into a film, is The Return of Martin Guerre, by Natalie Zemon Davis. For a better understand of how medieval society was structured, I would also recommend The Ties That Bound: Peasant Families in Medieval England by Barbara Hanawalt. Much of what Hanawalt describes is applicable elsewhere, and most people in medieval Europe were peasants! A little heavier, the book Myths of Renaissance Individualism by John Jeffries Martin talks about the longstanding idea that "the individual" and associated concepts of identity arose during the very late Middle Ages. The Discovery of the Individual: 1050-1200 by Colin Morris discusses the same issue, but more explicitly makes the case that "the individual" developed earlier than the Renaissance. If you have more specific interests about certain places, times, or groups, I can make more targeted recommendations.

I'm very much interested in the idea of identity in the Middle Ages, but I would like to know what you mean by the term in relation to this article. Can you tell us more about the content of the article and the central argument?

That said, something tells me that this author is homogenizing premodern times in order to make some sort of claim about modernity.