I don't like the term "genocide" here. That word gets tossed around too much in the modern world. The Romans treated the Carthaginians in much the same way as any other defeated foe: not too nicely, but also not in a manner meant to systematically eradicate their language and culture from the face of the earth. The fields of Carthage were not sown with salt, as the often-repeated story goes. It is true that the city, after 146 BCE, was in a period of sharp decline and partial abandonment, but a mere 150 years later, it was revitalized under a Roman scheme and well on its way to becoming one of the largest and most important cities in the Mediterranean.

On the Carthaginians: we know quite a bit. Though it is a bit dated now, the best single source to learn about Carthage is still Lancel's (translated) book Carthage (1995). There are gaps in the picture, of course, and very few Punic written texts survive, but Phoenician/Punic archaeology has undergone a major upturn since the 1960s, when the site of Carthage itself was declared a UNESCO protected zone and concerted rescue excavations were carried out there. In the succeeding decades, excavations have revealed quite a bit about the Punic phases of the city, going all the way back to her origins in the 9th century. This work has mostly been carried out by the Belgians (at Ghent, I believe) and by the Deutsches Archäologisches Institut. Excavations of Punic sites elsewhere have also contributed greatly, like the Carthaginian enclave at Motya (western Sicily) and the fascinating city of Kerkouanne on Cap Bon, with her circular city plan.

There is far too much material relevant to your question to write here. The best place to look is in Lancel's book. I will write about just one small aspect, since it is distinctly Phoenicio-Punic and certainly interesting. But in brief: Carthage was settled by Phoenicians, a sea-faring race from the Levant, in modern Lebanon. Their principal cities were Tyre and Sidon, and their language was Semitic in origin. Around the 9th century BCE, they began to make voyages to the western Mediterranean (probably in search of raw materials, especially metals, though this is a contentious topic). Archaeology now strongly indicates that Carthage was founded and flourishing by the middle of the 8th century, and was already a large and important hub in the central and western Mediterranean by that time. The core of her population seems to have been Semitic (that is, Phoenician), though it is likely that many different groups settled there, including Greeks. Archaeological investigation suggests that Carthage was an intermediary between raw material coming out of the West, especially the regions around Cadiz, and the Phoenician mother cities in the eastern Mediterranean. By the middle of the 6th century, links to the "motherland" were becoming less important, and Carthage was becoming a regional power in and of herself. This is typically when we start calling the city "Punic" instead of "Carthaginian." She was a sea power, a facilitator of trade, and a manufacturing hub, especially the manufacture of precious objects (gold, silver, jewelry, etc).

A tidbit on Punic religion: for millennia, the story of Carthaginian child sacrifice had been discounted as purely Roman propaganda. Excavations at Carthage, especially under Larry Stager et al, have now definitively proven that not only did child sacrifice happen at Carthage, but it happened much more frequently than anyone could have imagined. There was a special burial ground for these sacrificed infants, called the Tophet, and the tophet at Carthage has been systematically and thoroughly examined by modern archaeology. Similar burial grounds have also been found at Phoenician sites elsewhere in the West. The gods in question were Baal Hammon, roughly equivalent to Roman Jupiter, and to his consort Tanit. Tanit is a fascinating deity who deserves more than what I can write here, but she was a terrible and frightening goddess, associated with fertility and virginity (yep), and it is to her that we often find sacrificed children (via the inscriptions commemorating the act). She is in some way probably related to the familiar Phoenician goddess Astarte, though Tanit is a distinctly west-Mediterranean version of the goddess. She has her own glyph, found everywhere in the Punic west. I highly recommend anyone interested to check out Lancel's book, and also, for the Phoenicians, Markoe's book The Phoenicians. In both can be found a lot more about Phoenician and Carthaginian gods, culture, practices, the tophet, et cetera.