These are not "proxies" in the sense that Iran created any of them. Hamas and Hezbollah grew in the resistance to Israeli occupations and aggressions, and turned to Iran for arms. That doesn't mean Iran runs either.
The Mahdi Army is a laughable example, since it's not a proxy of Iran at all. They oppose Iranian influence in Iraq, and the Iranian proxy if anything is the Badr Brigades, nowadays largely known as the Interior Ministry. Iran has direct influence in the Bagdad government and an uneasy relationship with Moqtada and his Mahdi Army; even when it hosts him to stay on the good side of all Iraqi Shiites.
Wikipedia not bad:
Although Muqtada Al-Sadr has historically had close ties to Iran, he has generally opposed Iranian clerical and political influence in Iraq. Unlike the Al-Hakim family, of the Supreme Iraqi Islamic Council and many leaders of the Dawa party who fled to Iran following the Persian Gulf War and remained there in exile until the American invasion in 2003 Muqtada al-Sadr and his family remained in Iraq throughout Saddam's rule. The refusal to leave Iraq garnered the Sadr family much support during and after the collapse of Saddam's regime. Early 2006, al-Sadr pledged military support to Iran and other neighboring Islamic countries if they were to be attacked by a foreign nation.[28] Since then, however, Al-Sadr has opposed the Dawa Party, and in March 2008 Prime Minister Maliki ordered a major offensive targeting the Mahdi Army in Basra.[29]