Is it permissible for a woman who wears the niqab to take a picture with a male teacher, with a space between them, and then publish the picture for her female friends?

You should not have taken a picture with the male teacher, nor should you have shared it even among women, because the picture might spread and be seen by men, and fools might exploit it. Underestimating the act of photography can be an opening for Satan and a door to temptation, for Satan exploits opportunities to mislead humans. Allah Almighty says: "O you who have believed, do not follow the footsteps of Satan. And whoever follows the footsteps of Satan - indeed, he enjoins immorality and wrongdoing. And if not for the favor of Allah upon you and His mercy, not one of you would have been pure, ever, but Allah purifies whom He wills, and Allah is Hearing and Knowing."