Are "fag" and "emne" synonyms and interchangeable?
No, "emne" is subject.
"Fag" is mostly used about proffessions and trades, but also about a study.
"fagfolk"- the opposite of laymen.
I see you took the German as well. Would you say "fag" is like "das Fach" and "emne" like "das Thema?"
When is hvilke or hvilket/hvilken used?
It changes according to the subject, I believe. Hvilken for -en words, hvilket for -et words, and hvilke for plural words.
That sounds logical. Thanks for your clarification ;) I usually cheat by hovering over the word. It always shows the correct form but that's unfortunately not how you learn...
Not sure why it cannot be plural. Can someone explain how you would know?
You'd know because of the 'hvilket'. It reflects the gender of 'fag' (-et, singular). If it was plural, this would be 'hvilke'.