How does earning a Masters in Iceland differ from the US?
In Europe, to be admitted to a Master's program, there are normally quite formal requirements.  In particular, you need a Bachelor in a to-be-defined field.  If your Bachelor is from another university, or in your case even another country, someone will have to approve its equivalence.  That's usually not the professor's role (though their support might help to convince the relevant offices of the relevance of your background).

I would recommend to first contact the University's International Office, introduce to them what Bachelor you have from what university, to ask them what the procedure would be for you to enroll in the Master course.  

In Europe, a Master degree is typically one or two years including course work and a small (~6 months) research project.  You don't need to decide on the research project at time of enrollment, rather when you are already enrolled you can contact professors with ideas, or the professors may suggest ideas already.  Details vary.