I don't think Arcadi outranked Nick Jr. or Rocco Sollecito. Vito/Sollecito were supposedly best friends, grew up together, family from the same town, the whole 9 yards. Rocco was as close as family can be even IF they were not kin. Yes maybe by the rules of the rank he outranked Sollecito but I don't think Sollecito wanted the top spot either and that's why Arcadi went up instead. One thing we can agree on, this was a weird ass set up no matter what! But it does seem that Vito or Nick gave them all an option to take over when Vito went away, but maybe they all said no out of respect for Nick and when Arcadi said yes he took the role of "acting boss"? Hell who knows!
As for Nick Sr. I don't think he was ever "out". He was one of those like Peter Limone from the Patriarca's when he got filthy rich when he got out of prison but still wanted to be a gangster. I think Nick gave Vito advice when asked and I do think Vito gave his Father tribute. Whether it was his cut or not, who knows. But I do think his Father kept his hands dirty the whole time. I do think he slowed down of course before Vito went away, but after that things changed.
Great catch on Del Balso's house invasion being 2 days after Arcadi got out. That is very important, remember they tried to get his family to contact Del Balso and get him there. If they were willing to bust in blind like that, then they were possibly wanting to keep him alive to maybe get Arcadi as well. I don't think that timing means Arcadi went after Del Balso because I've always been under the impression Arcadi/Del Balso/Giordano were all close and had plans when they got out to take over after all that has happened. It's confusing to say the least.