"6) The spiritual power of the Church stands in judgement of the moral conduct of the temporal power of the state
7) This power is held by St. Peter and his successors by commandment of Christ giving power to bind and loose
8) It is necessary for salvation for all to be subject to St. Peter's successors."
As to 6 & 7, Orthodoxy believes this power is given to all the bishops who rightly teach The Faith (Matt 18:18). Orthodoxy I suppose accepts 8 in the sense that proper ecclesiology requires that the Pope of Rome be the "leader among (but not over) the bishops". On the other hand, the conclusion in 8 is at least arguably problematic from an Orthodox pov since +Peter's position as primus is quite clearly dependant on his profession of faith (Matt 17). If the Pope should abandon the Faith, then of course he cannot exercise that primacy. Certainly Rome doesn't believe it ever abandoned the Faith, but the other four patriarchates believe that is in fact what happened. It seems likely that both "sides" have "adjusted" their positions over the past 100 years or so; certainly the enthusiam one sees in Orthodoxy, even among educated laymen and lower clergy, for +BXVI would seem to indicate something of a sea change in relations between these particular churches. And I must say the respect and reverence for Orthodoxy evinced by so many Latin Rite Catholics bodes well for the future.
Western Catholics also recognize that nos. 6 and 7 apply to all bishops. Our claims for the bishop of Rome are that he exercise this kind of authority granted to all bishops but also stands at their head for the sake of a focus permitting unity to be maintained. His role of "confirming the brethren" (his brother bishops) is simply that--not lording over them but at their head for the sake unity leading the universal episcopal college and serving as the ultimate point of reference for resolving differences among them because unity is so important (Jn 17).
That, then, is the sense in which no. 8 applies. Adhering to Peter and his successors is another way of saying that the college of bishops, all of whom are authorized by Christ to govern in their dioceses in ways included under 6 and 7 and in a lot of other ways, voluntarily submits, in case of genuine disagreement among them, to Peter's successor for the sake of unity.
Cyprian already made clear that each bishop is a Peter in his own diocese and that they colletively bear responsibility for governing the Church, but that in the face of real schism and unresolved disagreement, Peter's successor as bishop of Rome has a special role, for the sake of unity. Exactly how that role gets played out (the details of Petrine jurisdiction), that's what we are arguing about most of the time. And it is not carried out the same way vis-a-vis the Roman rite as it is vis-a-vis the Eastern rite Catholics. And we recognize that it can benefit from further clarification. We just won't let go of the basic claim.
We would agree. See St. Thomas Becket, for example.
The Bishops have this power in virtue of their office, and hold their office by virtue of their union with St. Peter's See.