There might be some confusion as to the council in question. At least three representatives from the Western end of the church (two presbyters from Rome, and the Bishop of Cordova) attended the Council of Nicaea in 325; none attended the Council of Constantinople in 381. The former was meant to put an end to Arianism, but Arianism resurfaced, and was even ratified by the (later repudiated) Council of Alexandria in 362. This necessitated the Constantinopolitan council.
So coming back to the Nic/Const. councils, when they presented the answer to the Arian crisis Pope, he accepted it. When they said they would reign together (as co-equals), this was also correct (as far as I understand it). But since this was an issue of government of their respective churches it would not be protected by the charism of infallibility. Do I have this right?
As I understand it, the charism of infallibility depends upon the Pope teaching in accordance with the established pattern of faith. I.e., were a Pope to somehow proclaim that he was speaking ex cathedra when he said Jesus was entirely human and not at all divine, his statement would not be taken as being ex cathedra or as being infallible, because it would be in contradiction of established doctrine.
In respect to this matter of the councils, the charism of infallibility would also, I imagine, rest upon teaching in accordance with the rest of the church. Thus, I suppose that the decisions of the Council became properly ecumenical and a basis of infallibility only when the Pope and Western church agreed with them.
As an aside, hasn’t the ‘filioque’ issue been settled? If so what still separates us? If not, what’s the issue with the Spirit proceeding from the Son?
You would need to ask one of our Orthodox brethren those ones. I suspect, however, that it may still rest on ideas regarding universal authority.