Did the Prophet Muhammad (peace be upon him) perform Umrah, and is it permissible to perform Umrah on his behalf?

The Prophet (peace and blessings be upon him) performed four Umrahs.

Scholars have differed on the permissibility of dedicating acts of worship, such as Hajj and Umrah, to the Prophet (peace and blessings be upon him), with opinions ranging from prohibition to جواز (permissibility).