Is there a specific way to distinguish "Mig" and "med" when spoken or is it simply contextual? I may just have a comparatively untrained ear.
The TSS on this one is odd, making the 'p' of pratade sound like a 't', and the 'd' of med sound like an 'r'
"Mig" is usually pronounced "mej" and med "mæ", but you can easily miss the difference with an untrained ear.
"They spoke with her teacher" was marked incorrect. I now realise it is them talking about their own teacher. Does that seem right?
Yes, sin always refers back to the subject (=they), so it has to their own teacher and no one else’s.
why cannot 'sin' mean 'his' or 'her' ? as in the parents are talking about their child?
Because it has to refer back to the subject (=they). Had the subject been han or hon, it would have meant his or her. But that's not the case in this sentence.
De pratade med deras lärare is also 'They spoke with their teacher' in English. The difference is that sin means it's their own teacher, whereas deras means it's the teacher of some other "they-group".