I watched it recently (third time) and the plot was already more clear. A few questions remain, tough.

Where was Dominic Abbandando in this movie?

Who is the kind of bodyguard guy that is often around Michael? He looks a lot like Zasa?

What has Tom Hagen's son done after he left to Rome? I think I saw him after he left, but since he doesn't has recognizable head, I did't really know.

Who killed Cardinal Lamberto? Was it the Archbishop, or just someone ordered by Lucchese?

Did Lucchese really believe that Vincent was turning rat?

I also don't understand the major plot: Why were all the Church/maffia guys (Keinszig, Lucchese, ...) against the Corleone's?

Were Keinszig and the Archbishop allies?