I'll take a stab at answering this, but it's kind of hard to focus on one aspect. I'm a linguist, not strictly speaking a historian. But I've done work in historical linguistics.

This of course is very dependent on the region, but in general yes.

The most complicated issues with answering the question is how your define what constitutes a language versus a dialect, which is primarily a political and cultural issue. Comprehensibility would be the logical division of languages, but that exists in degrees, not in absolute terms, so those lines are arbitrary.

Most languages existed in what we call a dialect continuum where your neighbors sounded different, but you could understand them. But you couldn't necessarily understand your neighbor's neighbor, even though your neighbor could.

For one, the idea of "nations" didn't really exist yet, so there was A LOT of linguistic diversity. For example, when Napoleon started doing censuses, French (at the time, the language of Paris) was spoken natively by less than a quarter of the population (Check out The Story of French) and was understood by less than half of the people in modern day France. Most people spoke regional languages such as Basque, Breton, dialects of German, Italian, les Langues d'oc, and other dialects of langue d'oïl (of which the modern French language, a descendant of the Parisian dialect, is a member).

England was similar. English itself had many dialects and celtic languages were still very prevalent in their regions. In addition, as an island nation, many people people involved in seafaring had at least basic knowledge of French. Anyone involved with the upper classes would have basic knowledge of French.

Spain had Basque, Galician, Portuguese, Mozarabic, Castilian, Catalan, Aragonese, etc.

German and Italian only came to have a sense of a "national language" long after Goethe and Dante practically invented them. Before that it was a hugely diverse region of non-mutually comprehensible dialects.

The point of mentioning all these is that traveling or doing commerce across even very short distances often required a different language if not at least different vocabulary.

Upper classes were very often multilingual, especially women. Women were often from other regions for the purposes of alliances and the like, and so they often didn't share a language/dialect with their husband. This is partially the reason for the term "mother tongue" as it used to be distinguished from the language of the community (since the mother was often from elsewhere). This was especially true of royalty, who often imported princess from very different kingdoms across Europe. There are exceptions to this of course, but this was the general trend.

Merchants would very frequently have basic knowledge of other languages because of the nature of their job. We have lots of records of small phrasebooks and things of that nature. When lots of merchants were involved, they often created their own "language" such as lingua franca. In fact, so many people were familiar with this language in its day that it became the name for any neutral language two non-native speakers used.

Another key aspect of this was Latin. Anyone with even basic literacy (while extremely limited) would have knowledge of latin. And even if you weren't literate, you certainly went to mass so even the poorest of poor had exposure to Latin.

Peasants who didn't have the opportunity to leave their towns were the least likely to know another language. But they still got exposure, hence why English today has more French vocabulary than Anglo-Saxon vocabulary.

Also the language landscape changed frequently, so it seems that languages in general were easily learned. Gaul become Latinized very quickly so it doesn't seem that celtic speakers had much difficulty acquiring Latin (Romans even commented on how similar Gaulish was to Latin, so that probably helped). Etruscan was easily replaced by Latin, Basque and other (with a big question mark) languages of Iberia were quickly replaced as well. English uprooted Celtic, only to be subsequently imposed upon by Latin's daughter French. This would not be possible at that scale and frequency if language learning and bilingualism were not common.

Merchants would tend to have a main trading partner somewhere and would either learn the language of that region or carry around phrase books as we still do today. There are for example 14th century Italian-Dutch phrase books used to communicate to a very basic level.

In international diplomacy it often depended on the political context of the time. Spanish was very important on an international level during the Spanish Habsburg dominance. French followed as THE dominant language in international diplomacy during the period of French dominance under Louis XIV. Today it has become English due to England's and America's dominance.

In general however I think Latin should be seen as the most important of all. For most of the middle ages it was the clergy that read and wrote. They all spoke Latin making international correspondence in that language easy. When general education started to improve in the 1100s and 1200s lay men would also be taught Latin, further increasing the power of Latin as an international tool of communication.