Is it permissible for someone who is not a doctor to perform "hijama" (wet cupping), even if they are skilled at it? And is it permissible for it to be performed on women by someone who is not a doctor?

It is not a condition for the cupper to be a physician; rather, it is sufficient for him to be experienced in cupping. The jurists did not stipulate more than this, and they explicitly stated that a skilled cupper whose actions do not exceed the norm is not liable if the person being cupped has given permission. However, whoever practices medicine (cupping) without skill is liable. The general rule is for men to cup men and women to cup women, except out of necessity or need, in which case it is permissible to cup the opposite gender, provided certain controls are observed.