While I'm not aware of information on how frequent duels might have been during that time period, they did happen and they were part of the legal system at the time.

The "holmgang" was essentially a duel between individuals to settle disputes. The disputes could be over anything; land, insults, property, titles, legal matters, etc.

In theory, anyone could challenge anyone else but you could have a substitute fight for you if you were clearly out-classed. The exact rules differ from place to place and they were generally agreed upon by the combatants beforehand.

Such fights were quite important because being challenged represented the very real possibility of injury, death, or being expelled (they referred to it as "outlawry"). We don't have much first-hand information about them, much of what we know comes second-hand and there are stories about them being "to the death" but as rules were decided by the combatants it's probable that death was not common. We have sources from the 13th century (which is ~200 years after these duels even took place so take them with as much weight as you feel warranted) that mention that weregild (a price paid to the family of a slain person, highly dependent on their social rank) was to be paid if the challenger won, however that source is regarding a challenge over an insult.

Interestingly, we do have information that these duels could be and often were exploited by skilled fighters. Egil's Saga actually mentions a man by the name of Ljot who was not cast in a favorable light for doing just that. Holmgang was basically outlawed in the very beginning of the 11th century largely due to such reasons.

The Saga also talks about a holmgang between Ljot and Egil but doesn't go into detail about the actual event itself, likely because the audience for Egil's Saga would have been familiar with the process and wouldn't need it explained.