Short answers, pulled from the story.
Punic is an extinct variety of the Phoenician language, belonging to the Canaanite branch of Northwest Semitic. It was principally spoken on the Mediterranean coast of Northwest Africa, the Iberian Peninsula, and several Mediterranean islands, from the 8th century BC to at least the 6th century AD.
Punic is generally considered to have survived into at least the 5th century AD, long after the destruction of Carthage in 146 BC. Augustine of Hippo wrote around 401 that people in northern Africa were still speaking it. Trilingual gravestones in the catacombs of Sirte, Libya, and later descriptions by the geographer al-Bakri suggest the spoken language may have outlasted even the Muslim conquest of the Maghreb.
Augustine of Hippo, who died in 430, is considered the last major ancient writer with knowledge of Punic. Around 401, he wrote a defense of the language, arguing it had preserved many things wisely in books, and reported that people in his region of northern Africa still spoke it and called themselves "chanani," meaning Canaanites.
Neo-Punic is the dialect of Punic that developed after the Roman destruction of Carthage in 146 BC. It differs from earlier Punic in its spelling and in its adoption of non-Semitic names of Libyco-Berber or Iberian origin, reflecting contact with northern Berber peoples. The historian Sallust described it as having been "altered by their intermarriages with the Numidians."
Punic pronunciation is reconstructed primarily from texts written in Latin or Greek characters, including inscriptions and the comedy Poenulus by the Roman playwright Plautus. Poenulus is especially valuable because its Punic lines largely preserve vowels, unlike stone inscriptions that omit them. The Cippi of Melqart, bilingual stone pillars found on Malta, were also integral to the decipherment of the language.
No. Modern linguistics has established that Maltese descends from Arabic, most likely Siculo-Arabic, with a large number of Italian loanwords. The idea that Maltese descended from Punic was first proposed in 1565 but has since been disproved. Punic was spoken on Malta, as evidenced by inscriptions found there, but it is not the ancestor of Maltese.