Mu’ta in Islam is a secondary option when a person due to different genuine reasons can’t to permanent marriage do Mu’ta but we can’t make Mu’ta as a tool of lust. Also there is a culture in some families they do Mu’ta before permanent marriage in order to bride and groom understand each other but they refrain from having sex( it’s conditional otherwise if there no prior condition has been set, they can live life like a husband and wife) but in all cases if girl has father or if father is not alive grandfather and she is not married doesn’t matter how old she is has to take permission from her father. But if there is no wali alive, she can take her decision on her own unless her father has not made anyone as her guardian.