Has there ever been any examples of rival cliques in family's between american, northern, Sicilian zip, Calabrian factions? Apart from donnie brasco with the bonnanos ha. Also is there any other regions of Italy that have been accepted in to lcn like Sardinians maybe?

Sardinians haven't emigrated in large numbers in america; as I know the Gotti was called the neapoletan crew,against the sicilian gambino or Scarfo Sr., who said to an his ally, that they that were from Calabria, had to protect themselves in that sea of Sicilians.
Or the Montreal war between sicilians and calabrians.

never heard of sardinians inducted in the mafia they have a sort of their own banditry and even in italy they are considered ordinary gangs but not organized crime

First question's first...Neapolitans and Sicilians all the time. Off the top of my head, John Bazzano of PIttsburgh circa 1932 assassinated several Neapolitan gangsters in his city. The Commission felt he needed permission. He was "called on the carpet" in Brooklyn by Anastasia, Santo Volpe, and others and asked to explain himself. Rather than talk himself out of a death sentence, he angrily wished death on all of the Neapolitans and was stabbed with icepicks until he bled to death.

The killing had huge reverberations. Frank Milano, the don of Cleveland was known to be a backer of John Bazzano and wished to increase his regional influence, one of the early examples of a cycle of conflict and uneasy cooperation between the two cities. Milano fled Cleveland soon after for Mexico. Bear in mind, contrary to popular belief, Stefano Magaddino's eventual place on the Commission was originally given to Frank Milano. So for inflaming ethnic tensions Frank Milano suffered a huge blow in prestige, and a Commission member left the rackets behind. That's my opinion at least, Milano was also under indictment. Some books disagree about which caused it, but yeah it was a very big deal.

Neapolitan Camorra war earlier. They wanted to avoid it happening again. In general from what I've read, Sicilians had a difficult time getting along with Northern Italians as well because culturally they were much different.

As for conflict between zips and Americans, Galante stands out, but that was not for ethnic reasons. The American faction feared the zips for sure. They did business in a more brutal manner.