"The CIA has publicly admitted for the first time that it was behind the notorious 1953 coup against Iran's democratically elected prime minister Mohammad Mosaddeq," Please read the rest of the article here: 

https://www.theguardian.com/world/2013/aug/19/cia-admits-role-1953-iranian-coup

In 1976 the oil contracts between Iran and the big powers mainly Great Britain ended and Iran wanted to renew the contracts for mutual benefit not just to be one sided.  GB fooled the US into overturning the Shah and put the Ayatollahs in charge!  It was a total loss!

The US and European nations realized their mistake and asked "Saddam Hossein" a puppet, for help.  They gave Saddam chemical weapons, missiles, planes, tanks, logistics, etc to hit Iran.  Close to 1 million civilians died as a result.  

I believe Lebanese Hezbollah branch acted on its own without any orders from the Iranians.  remember the Iranians were fighting Saddam Hussein at the time and were pretty busy getting hammered.