What is the definition of "permissibility of sin" (istihlal al-ma'siya), and do the actions of the questioner—repeated masturbation, or committing a sin while knowing it is forbidden, or being ignorant of its prohibition—constitute a form of "permissibility of sin"?

Considering sins permissible is the belief that what is Haram (forbidden) by consensus is permissible, such as someone believing that pork or adultery is lawful. This necessitates a judgment of disbelief (kufr). What you mentioned about masturbation or committing sins out of ignorance of their prohibition is not considered deeming them permissible. We advise you to marry as a cure, and it is not permissible to seek a cure through theed forbidden act of masturbation.