It depends on the teacher.
Some of my teachers were native English speakers, some of them weren't, but were perfectly fluent, and some weren't fluent at all.
There isn't a particular rule about it, it only depends on the school's appreciation of the teachers qualification to teach English.
Same thing for the unusual sounds, some teachers will insist on it, and some won't.
It doesn't mean they will succeed, though. For example, several of my teachers insisted on word stress (which doesn't exist in French), but most of my then classmates never even understood there was a concept of word stress to begin with.