What is the Shar'i definition of Khul', is the husband's consent a condition for it, and what is the solution if the husband refuses?

It is recommended for the husband to accept his wife's request for khulʿ (divorce at the wife's instance, typically by returning the mahr), especially when the continuation of marital life is impossible. If the husband refuses, the wife has the right to resort to the Sharia courts, so that the judge may rule as he deems appropriate. It must be noted that a woman is not permitted to request a divorce from her husband unless she is severely harmed by remaining with him; otherwise, she would be wronging herself and exposing herself to Allah's torment. The Prophet, peace be upon him, said: "Any woman who asks her husband for divorce without any strong reason, the scent of Paradise will be forbidden to her," and "A woman should not ask her husband for divorce without justification, lest she fail to find the scent of Paradise, though its scent can be found from a distance of forty years."