"Múinteoir is ea an fear."
Translation:The man is a teacher.
This is a somewhat strange word order to me, I would say "Is múinteoir é an fear". Does it matter at all, or is this another regional thing?
Múinteoir is ea an fear, puts more emphasis on múinteoir. That is it is a version of "Is múinteoir é an fear" with more emphasis on "múinteoir".
In the South however it is the normal version of the sentence and "Is múinteoir é an fear" isn't really said.
Exactly. This is just a way to stress that he's a teacher. It'd be like "He's a teacher", with extra stress on teacher, in English.