And they made a deal with AQ back in the 90s to have them trained by their Hezbollah mercenaries. They even helped a lot of their fighters escape Iraq before the war.
In the early 90s Al-Qaeda was not a terrorist group. Al-Qaeda was actually financed by the CIA as well.
Are you talking about the Iraq-Iran war or the US invasion of Iraq, because the latter could actually be considered sponsoring terrorism?
BTW, HEZ is a terrorist group based out of Lebanon. Iran started funding them to fuck with Israel. Hell, their manifesto talks about the destruction of America, the French and jews.
It does not matter what their agenda says.
As long as they are not systematically killing civilians in a terror campaign, they are not terrorists. Hezbollah has no major record of attacking civilian targets, whereas Israel does.
I acknowledge that Iran does fund Hamas though (since they admit to it), so I will concede that Iran sponsors terrorism abroad.