What is the ruling on permanently removing thick, excess facial hair if it resembles men's hair, and is there any medical harm in removing it?

The basic principle is that it is not permissible for a woman to remove facial hair, as it is considered namṣ (plucking), which is forbidden. However, if it reaches a degree that disfigures her appearance, then it is permissible to remove it or remove the excess of it, to alleviate harm and hardship. As for permanent removal, this should be referred to a knowledgeable doctor; if he determines it to be harmful, it should be avoided, but if there is no harm in it, then there is no objection.