What's the difference between "Hun er rørlegger av fag" and "Hun er rørlegger"? I'm a native speaker of English, and I'm not completely convinced I understand "by trade". I think it means "Despite what she happens to be doing at the moment, she is a plumber by training and experience."
Speaking of German, I don't know whether this was an intentional reference to the song or not, but I can't help but think of this ...
Ich bin Klempner von Beruf,
Ein Dreifach hoch dem, der diese goldene Handwerk schuf ...
Denn auch in den grøßten Nøten gibt es immer was zu løten,
es gibt immer wieder Pannen an WCs und Badewannen,
ich bin Klempner von Beruf.
Just one of Reinhard Mey's many genius works of lyrical art. And he looks pretty kjekk here, too. :-)
Fag = English 'Fack', a defined space or interval. The meaning has definitely changed over time since Proto-Germanic but I can kind of see the meaning when you consider one's trade as how they spend an allotted time. So 'Hún er rørlegger av fag' = 'She is a rushlayer by fack'.
This means that she has an education and an apprenticeship leading to a diploma. However this sentence will usually indicate that she has another profession. She is the CEO of the construction company and a plumber of trade. If you want to say she is a plumber by profession you say: Hun er rørlegger av yrke