Did you just miss the part where I said the operation was not limited to Kirkuk, but included Nineveh, Sinjar where there is no PUK but Barzani the lapdog of Turkey.
So? It also included mixed Kurdish/Shia Turkmen cities where the presence of Iranian-allied militias have been documented. You seem to forget that the KRG faced similar pressure from Turkey, which cooperated its move together with Iran, with the tacit support from Baghdad.
IRGC isn't experienced in urban or infantry warfare so do yourself a favor and keep to your side. All this interference has been possible due to Iraq being Shi'a and generally friendly to Iran as opposed to Saudi Arabia not having influence. Iran has major weaknesses which you like to ignore to prop up this false image of strength.
What are you talking about? The IRGC has tremendous organization experience in warfare due to the support it has delivered to Hezbollah, which is basically an IRGC division, as well as the experiences it has gained from the Syrian Civil War.
All this influence is only possible because Iran has managed to sucesfully operate in a complex geopolitical theatre of Iraq, knowing how to organize, motivate and operate all kinds of militant groups in a sea of anarchy and instability. It perfectly knew how to militarily and politically pressure the United States during its occupation of Iraq, being a significant reason why the US failed in its goals and eventually had to pack its bags.
If you think that what the IRGC does is simple, you don't know what you are talking about. It's hybrid politico-military way of warfare, which has created the most powerful and competent non-state military force in the world (Hezbollah), even surpassing many regional national armies in competence, is purely an Iranian creation. It's extensive logistical presence in the region is something no regional power has managed to copy. Its capability to transform its proxies into effective forces has been credited by US military officials as top-notch. With limited military resources, at its highest operating no more than 1000 military officials, Iran managed to save Syria from falling in the hands of rebel groups, who nearly managed to destroy the Syrian army, from within and the outside.
In Iraq, it were first the Iranian-allied groups who managed to stop IS from further advancing. It were these groups, under the supervision of Iranian officers, that engaged IS when Iraqi security forces were crumbling. This happened at a time when the US refused to intervene, calling for Maliki to step down before it lends support. You seem to forget all these things. Iran was a huge reason why Iraq survived eventually, next to the US of course.