No non-Latin prayers in European churches before Reformation?

Not all: Saints Cyril and Methodius and the Moravian Church

Note that this happened before the Schism between Rome and Constantinople.

In 867, Pope Nicholas I invited the brothers to Rome. Their evangelizing mission in Moravia had by this time become the focus of a dispute with Theotmar, the Archbishop of Salzburg and bishop of Passau, who claimed ecclesiastical control of the same territory and wished to see it use the Latin liturgy exclusively. Travelling with the relics of Saint Clement and a retinue of disciples, and passing through Pannonia (the Balaton Principality), where they were well received by Prince Koceľ (Kocelj, Kozel), they arrived in Rome in 868, where they were warmly received. This was partly due to their bringing with them the relics of Saint Clement; the rivalry with Constantinople as to the jurisdiction over the territory of the Slavs would incline Rome to value the brothers and their influence.

Their project in Moravia found support from Pope Adrian II, who formally authorized the use of the new Slavic liturgy.

Subsequently Methodius was ordained as priest by the pope himself, and five Slavic disciples were ordained as priests (Saint Gorazd, Saint Clement of Ohrid and Saint Naum) and as deacons (Saint Angelar and Saint Sava) by the prominent bishops Formosus and Gauderic. The newly made priests officiated in their own languages at the altars of some of the principal churches.

Later on, Methodius ran into some trouble in Pannonia (Northern Italy/Southern Austria) and his efforts to establish the Slavic mass failed there.

While I used Wikipedia as a source, most of their efforts are acknowledged by both the Greek Orthodox and Roman Catholic Churches. From Catholic.org.

The brothers' first appearance in a papal document is in Grande Munus of Leo XIII in 1880. They are known as the "Apostles of the Slavs", and are still highly regarded by both Roman Catholic and Orthodox Christians. Their feast day is currently celebrated on 14 February in the Roman Catholic Church (to coincide with the date of St Cyril's death); on 11 May in the Eastern Orthodox Church (though for Eastern Orthodox Churches which use the Julian Calendar this is 24 May according to the Gregorian calendar); and on 7 July according to the old sanctoral calendar that existed before the revisions of the Second Vatican Council. The celebration also commemorates the introduction of literacy and the preaching of the gospels in the Slavonic language by the brothers. The brothers were declared "Patrons of Europe" in 1980

No non-Latin prayers in European Catholic Churches before Reformation?

Is this true that before the Reformation, all Christians in Europe would have to study Latin in order to understand the prayers pronounced during Masses in Roman Catholic Churches?

The short answer is no, for two reasons.

The first reason is quite simple. A large percentage of the faithful could not study Latin because they were illiterate.

The Reformation dawned on European societies where literacy was restricted. At the end of the Middle Ages, the ability to write was restricted to less than 10% of men and hardly any women possessed it. This fundamental division between the sexes persisted for centuries and throughout the early modern period male achievements almost always overshadowed those by women. For example, one bridegroom in three could not sign Amsterdam's marriage register in 1630 compared with two-thirds of brides. Until the eighteenth century the rate of improvement for men generally exceeded that for women, so that the gap between the sexes seldom narrowed. Amsterdam brides and grooms both saw illiteracy fall between 1680 and 1780: males from 30% illiteracy to 15% and females from 56% to 36%.14 The literacy of townspeople also grew more quickly than that of rural dwellers and the wealthier merchants and professionals inhabited city centers where concentrations of reading and writing ability were especially high, distinguishing them even from suburban dwellers. By the mid-eighteenth century London and Paris had literacy levels of over 90%, which would not be achieved nationally until the late nineteenth century. In Eastern and Southern Europe nearly the only literate people were town dwellers and rural landowners. - Introduction: The Literacies of Early Modern Europe

The second reason is completely different. Although the Mass of the Roman Rite was Latin in churches of the Roman Catholic Church, exceptions were permitted by Rome.

The Roman Rite is used in Dalmatia in an Old Slavonic version (written in Glagolitic letters), occasionally in Greek in Italy; but in any language it is always the Roman Rite. - Catholic Encyclopedia

In other words, the exact same Mass could be said in at least three languages: Latin, Greek and Old Slavonic and thus were considered Roman Catholic and not Eastern Rite Catholics. Please note that some authors employ the term Greek Rite or Old Slavonic Rite, but in this case, the term means a variation or usage of the Roman Rite.