Short answers, pulled from the story.
The Third Punic War began when a Carthaginian army under Hasdrubal marched against King Masinissa of Numidia, violating the peace treaty signed in 201 BC. This illicit military action provided Anti-Carthaginian factions within the Roman Senate with a pretext to prepare a punitive expedition.
Scipio Aemilianus gained sole command because public demand was so strong that the Senate put aside age requirements for all posts for the year. He was elected consul despite being aged 36 or 37 since the minimum age was 41 and granted unusual entitlements to enroll volunteers and conscript men.
Roman forces breached the walls of Carthage in the spring of 146 BC after launching a full-scale assault from the harbour area. Over six days they systematically worked through the residential part of the city killing everyone they encountered before setting buildings on fire.
The historian Polybius accompanied Scipio Aemilianus in North Africa during the Third Punic War and is the main source for most aspects of the conflict. His work The Histories was written sometime after 146 BC, though significant portions have been lost and modern historians also use the account of Appian.
Rome determined that the city of Carthage remain in ruins so the Senate despatched a ten-man commission to carry out further demolitions. A curse was placed on anyone who might attempt to resettle the site in the future while the former territory became the Roman province of Africa with Utica as its capital.