Is it permissible to bear false witness, and even to swear to it, in order to restore a right to its owner that was taken from him by fraud, and what is the ruling on resorting to man-made courts to obtain a right?

Giving false testimony is one of the major sins, even if the intention behind it is to reach the truth, because the means must be legitimate.

Resorting to man-made laws that contradict Islamic law is forbidden. If a Muslim willingly and voluntarily does so, he may commit an act of disbelief (kufr). However, if he is compelled to do so due to the absence of Sharia courts and the potential loss of his rights, it is permissible under certain conditions: that the right itself is legitimate, that he cannot access it except through this means, and that he does not take more than what is rightfully his.