Wat was the deal then about Altobello? Was he a Corleone-friend who took over the Barzini, Tattaglia, Cuneo, or Stracci familiy?

Or...maybe has was Capo of the 6th family.
There you go Plaw, I solved your mistery.
There are indeed 6 families. But the sixth worked somehow together with the Corleone. So they weren't punished in the 5-families-murder.
Zasa was a capo, or underboss that eventually took over the family after Altobello retired on a way Vito also did.