Under what conditions is nikkah mutah allowed and with who?

First of all we should understand that Mutah is not just only for removing ones sexual desire. Secondly the main condition for Mutah is that if the girl is virgin she must have permission from her guardian either her father or her grandfather. Secondly she must be either Muslim or Ahle Kitab( Jews or Christian) thirdly if a person is married in permanent marriage then he has to ask for permission from his wife.