Not true. Septimium Severus, a later Emperor, was partly of Punic descent. The Carthaginians had a huge empire, with many subordinate cities. Most of them were not destroyed in the way Carthage was.
Arabs are Hamitic, not Semitic.
Not true, unless you make up your own definitions. According to the Bible, Arabs are descended from Ishmael, Abraham's other son.
They also speak a Semitic language, quite closely related to Hebrew.