The modern "research university," in which undergraduate tuition and teaching is used to subsidize faculty research and graduate education, with great amounts of freedom afforded both students and faculty, is usually dated to the "Humboldt model" of the 19th century, starting with the University of Berlin in 1810. As with any institutional practice in history, there are antecedents one can point to, but it was this Prussian/German approach that other countries began to explicitly emulate. It is not that teaching or research did not exist in universities prior to this, but it was in the 19th century that this explicitly integrated model became the standard operating model for Western universities, as opposed to many other models that were being used at the time. (Even then, it took well into the 20th century for it to become truly "standard.")

Paper publishing began much earlier, as an outgrowth of largely correspondence based communication between scholars, and the emergence of scientific societies (the first "journals" were "proceedings of the society," which also included letters that people wrote into the society), like the Royal Society of London. By the 17th century this sort of thing was emerging.

Peer review is a more complicated story; though variations on it can be found fairly early on, it is not until the 20th century that it became considered the routine "gold standard." My friend Lindy Baldwin has written a great overview of the history of peer review here.

All of which is to say: the university of the last 100 years is fairly recognizable to modern practitioners, but the universities older than that, and scholarship in general, were pretty different. Many things that are held up as part of the "medieval" system of universities are actually quite modern. Much of what we think of as the modern institution of scientific research is remarkably recent, despite many centuries of antecedents.

(I don't know when formal academic conferences became a norm. That's a good question. I suspect not until the early 20th century. But that is just a guess.)