To what extent is it permissible to work in teaching newly introduced administrative law subjects such as labor law or the law of antiquities, and to work as an insurance broker, knowing the prohibition of teaching man-made law?

It is permissible to teach administrative law, as long as it does not contradict the Sharia, or while clarifying its errors and explaining what is correct according to Sharia. As for working as an insurance broker, it is permissible if it is Islamic cooperative insurance, and it is forbidden if it is commercial insurance, because it constitutes aiding in sin. Whoever abandons the forbidden seeking what is lawful, Allah will compensate him with something better and provide for him from sources he never anticipated.