First, about the Varangian Guards: It wasn't uncommon for non-Byzantines to be a part of the Varangian Guard. In fact, they were originally from Sweden or Nordic countries. (source 1, source 2) This has two main causes. One was Emperor Basil II's distrust of Byzantines. That sounds backwards since he was himself Byzantine, but by looking at his history, it makes sense. He had been through rebellions and backstabbings and crusades and more. Through all of that, he had learned to not necessarily trust the Byzantines. He had, however, seen Varangians in Rus (Kiev), and knew that they were reliable. The second reason is that, even though they were Swedes, they weren't always coming from Sweden or whatever Nordic country. Often times, members of the Varangian Guard were came from other militaries. For example, the original Varangian Guard wasn't sent from Northern Europe; they were sent from Kiev (actually as a wedding dowry, but that's not really important here). So, saying that a Swede went to the Byzantine Empire to join the guard wouldn't be entirely accurate. They were probably already active in the area.

Second, about the connectivity of Europe in the 1000s: A lot of Europe was connected, and there was lots of travel throughout many countries. The biggest reason, as it often is, was Christianity. The Holy Roman Empire, Kiev, and the Byzantine Empire were some of the most evangelical nations at the time, so they were often spreading the reach of Christianity. Another major contributor to Europe's connectivity was the Kingdom of Hungary. They acted as a major link between the Holy Roman Empire (headed by King Stephen of Hungary's brother-in-law Henry II) and the rest of Europe. The Byzantine Empire's connection to this was through Otto Orseolo of Venice, who was King Stephen of Hungary's sister's husband and also a close ally of Emperor Basil II of the Byzantine Empire, who, you guessed it, was the one who founded the Varangian Guard of the Byzantine Empire.

Another thing to note would be that these relationships were changing constantly. However, the concept remained the same: Christians want to spread Christianity and they like other people who agree with them. So, as long as Christians were moving throughout Europe, Northern Europeans would have had a chance to connect with Southern Europeans. The exact countries that were allied together may have changed decade-to-decade, but it all worked the same way.

tl;dr: A combination of Christianity and alliances made it possible for most of Europe to be somewhat connected