Is it permissible to open free boxes whose contents are unknown, and is it permissible to sell non-free boxes (closed boxes without opening them), knowing that opening them requires payment?

It is not permissible to sell boxes of unknown content, because knowledge of the content is a condition for the validity of the sale. Such ignorance is a form of gharar (uncertainty) which is prohibited by Islamic law. However, it is permissible to accept them for free, even if their content is unknown.