Does the Scrum Master need to know the team's expertise or not?

Yes, the Scrum Master needs to understand the team’s work and expertise, because the Scrum Master is accountable for the effectiveness of the Scrum Team. A Scrum Master cannot improve a system they do not understand. Without knowing the team’s work and expertise, the Scrum Master cannot spot impediments, bottlenecks, skill constraints, poor slicing, or misalignment with goals. That turns Scrum into task tracking instead of empiricism and learning.

The Scrum Master should not track or manage the work like a Project Manager. If a Scrum Master only checks whether work is done, they are doing administrative oversight, not Scrum Mastery. The Scrum Master’s job is to improve how the team works and learns, which requires enough understanding of the domain and skills to spot impediments, misalignment, and risks, without directing the work itself.

The Scrum Master only keeps track of whether the work has been completed or not. 

The Developers ought to monitor their own progress during a Sprint: it isn't the Scrum Master's job to do that.

But he has no information about what the work is for and what should be important. Does the Scrum Master need to know about the work done in the team or is it enough to just keep track of the work?

The Scrum Master needs to know enough about the work to have a nice warm fuzzy feeling inside that if it was to be completed, a Done increment would be produced that meets the Sprint Goal. That is the level of technical expertise required. A Scrum Master doesn't need to do the work themselves unless they are also a Developer. But if the Scrum Master is not satisfied that the Developers' commitments are likely to be met, how can they be sure that anybody is?