Translation:My mother comes from Iran and teaches me Farsi.
Er De også halv-Perser, som meg? Moren min kommer fra Iran.
How is it that " lærer bort" or "underviser" in not used here instead of " lærer meg"? Would it still be correct? Jeg lærer norsk. I learn (am learning) Norwegian. Jeg lærer bort deg norsk. I am teaching you Norwegian. Jeg lærer deg norsk. I am teaching you Norwegian.
Is this correct?
When the object of the sentence is a person, then it's obvious that they're the ones being taught something, so no further clarification is needed. You could also phrase it like example number two below, but it would be a less elegant way of phrasing it (just like it would in English).
"Å undervise" is mostly used in the context of a school or university; referring to classroom teaching, organised teaching. If I were a Norwegian teacher employed at a school, I'd say "Jeg underviser i norsk".
"Å lære bort" can be used in all contexts, but usually when the recipient of the knowledge that is being imparted is not mentioned: "Før jeg dør, vil jeg lære bort alt jeg kan". It can be tricky to translate directly, but deals with imparting knowledge.
"Moren min lærer meg persisk." (My mother teaches me Persian.)
"Moren min lærer bort persisk til meg." (My mother teaches Persian to me.)
"Moren min underviser i persisk." (My mother teaches Persian.)
"Moren min lærer persisk." (My mother is learning Persian.)
"Moren min lærer persisk av meg." (My mother is learning Persian from me.)