The an is before "woman" not "teacher". Also, note that this is emphasis (the woman is a teacher)
Close. It'd be Is múinteoir í an bhean, since with a definite noun, the object pronoun is needed.
But, yes, that would work. And there is a difference between the two phrases, with the one given by the problem Múinteoir is ea an bhean being emphasis ("The woman is a teacher")
I too put "The teacher is a woman". I knew there was no "an" before teacher but I just didn't understand to turn the whole sentence around. I kept thinking that made it a question but, of course, it doesn't. It is always odd for me that I can't translate a sentence in Irish without hearing the whole sentence. You can't translate as you read the sentence.