Have I erred legally by slapping and cursing this young woman after she falsely swore by God that she did not steal, even though I saw her stealing via the camera?

It is forbidden to entertain evil suspicions about a Muslim and to spy on them, unless there is a fear of missing the opportunity to prevent the violation of sacred prohibitions such as adultery and murder. However, in cases of theft, it is not permissible to set a trap. Beating and insulting a female thief is an injustice, especially striking the face, which is prohibited. It would have been possible to refer her case to the responsible authorities if her theft was proven.