There are probably competing interests in Iran over the conditions in Iraq.
There is the revenge thing for the First Gulf War (Iran-Iraq....Iraq vs U.S. considerd 2nd Gulf War over there.....). Revenge, feuds, and blood oaths/debts cross generational lines over there for many people. Plus, Iranians are mostly Persian, not Arabic like Iraqis.
There have been agents from Iran helping the Iraqi Insurgency with funds, training, and materials, as well as other agents from Iran encouraging the Shia on the political front..... could be coordinated efforts, but more likely competing interests in Iran with different goals.
Seeing the possibility in 2003-2004 of a neighboring Iraqi government being friendly toward the U.S. and alowing basing rights in Iraq had to make for....strong opinions... in Iran, especially after finding out they were part of the "axis of evil" (prior to *that* ***(personal opinion of speech deleted)*** State of the Union speech, there had actually been some inroads to normallizing relations between the US and Iran to the point of talk of reopening the US embassy in Iran.....doh!).
So, be it a choice of a U.S. ally or a raging civil war on their western border, I'd guess they'd pick civil war and try to profit by it in some way.
As to the Gloden Dome.....I don't see it as Iranian, that's one of their own holy sites IIRC in Sunni-dominated Sammara (used to see it in the distance while on convoys along Sammara bypass), and there have been large numbers of pilgrams from Iran visiting holy sites all over Iraq since the borders have been opened......It could have been the Insurgency, it could have been the extra-national terrorists, it could have been funded by Jordanian or Syrian or Saudi sources.....
I haven't really been following the news too closely in the states on it. I found very little in common in the details of national news reports as compared to what I was actually seeing on the ground during my tour in Iraq. News media is concerned with ratings and catchy talking points and keeping it simple for the lowest common denominator of viewer...... real world is far more complicated.