Also, were Phoenician Carthaginians a mixture of Phoenician and Berber heritage?
Carthage was founded by Phoenician settlers from the city of Tyre. The Canaans (Kn'nm) as they called themselves, were known variously as the Ponim (to the isrealites), Phoenices (to the greeks), Poeni (to the Romans).
Carthage is just "new city" in Phoenician, "Qart-hadhasht". It was Carthago to the Romans, Carchedon to the greeks.
Carthage created colonies of their own, and the inhabitants of such towns, like Utica and Hadrumentum, were known to the Romans as Libyphoenicians, after the mixed race quality from intermarriage between Carthaginians and Libyans.
Diodorus mentions that Carthaginians and Libyphoenicians could freely intermarry.
Carthaginian citizenship is a somewhat obscure topic, there are some indications that it could have been a two tiered system, possibly of freed slaves-turned citizens vs freeborn citizens. Another possibility is a division between citizens who could trace their ancestry to the Tyrian settlers vs everyone else. In a communique between Hannibal and Philip V of Macedon, Hannibal is at one point referred to as "kyrious Karchedonious", which has been suggested to be a copy error of "Tyrious Karchedonious", or "Carthaginian of/from Tyre".