The descendants of the Carthaginians would be the modern day Lebonese. The Carthaginians were of Phoenician descent who were a people who lived off of the coast of the levant. Carthage was set up as a colony from its mother city of Tyr. After Tyr was sacked by Alexander the Great, Carthage likely became a free city at that time. The Phoenicians were also called Canaanites.

Sources:

Carthage Must Be Destroyed by Richard Miles

The Romans themselves conquered up to the mountains of North Africa and had a client kingdom named Mauritania for the inland mountainous regions. I know there was a revolt issue sometime during the reign of Caligula (1st century AD) and I am not sure if it remained part of the empire after that. The climate and natural barriers would be why they would not have advanced further south for the North African area. As far as Egypt and the Horn of Africa, it again was likely climate and natural barriers. Both areas had highly mountainous terrain and extremely hot deserts that would have made crossing, let alone campaigning, fairly dangerous and not worth the resources.