Although there's certainly more to be said (especially given your multi-part question) you might be interested in this very cursory answer of mine mostly focusing on the Italian dimension of confrontations between secular and religious authorities, also examining the Papacy's assertion of temporal power in central Italy.

In many ways, you'll see in that answer, the Papal States were probably the least efficient polity in Italy (and probably the most unstable) but importantly their existence was seeped in the Italian political tradition which in its earliest form equated religious with political authority. The slow but unmistakable transition away from this system, in Italy at least, was in many ways what framed many conflicts between secular rulers and the Papal States: the War of the League of Cambrai against the Republic of Venice, for example, was started on the pretext of the Republic of Venice running its own church as it pleased (although the deeper causes, as you might imagine, were much more complex). But for the citizens of Venice, their Republic held the moral high ground. Think of it this way: for the Venetians, arguing that St. Peter's seat in Rome is more important than St. Mark's in Venice is exactly what that power-hungry Pope would say. You can read more about that here.

Of course, I'd also be more than happy to answer follow-ups.