Short answers, pulled from the story.
Colonies in antiquity were city-states founded from a mother-city, or metropolis, rather than claimed from open territory. Greek colonies of the Archaic and Classical eras were sovereign and self-governing from their founding, while Phoenician, Roman, Carthaginian and Han Chinese colonies typically stayed tied to their home city or empire.
Carthage was founded by settlers from Tyre in 814 or 813 BC under the name Kart-Hadasht, meaning New Town. Radiocarbon dating from its earliest layers points to a founding between 835 and 800 cal BC, matching the dates recorded by the ancient historians Flavius Josephus and Timaeus.
Ancient Greek colonies formed for several reasons, including escaping subjugation after a military defeat, resolving civil disorder, relieving population pressure at home, and following ostracism. In most cases, though, founders aimed to open trade relations and grow the wealth of the mother-city.
Roman colonies functioned as citizen garrisons planted in conquered towns to secure territory, since Rome had no standing army in its early republic. Unlike self-governing Greek colonies, Roman coloniae adopted a constitution copied from Rome's own and were founded by a commission of patrons, with colonists receiving a share of conquered land.
Historians debate how much credit belongs to Sabaeans from Sheba in South Arabia for the founding of Dʿmt around 800 BCE near Ethiopia's Tigray region. Evidence includes Sabaic inscriptions and Sabaean-style temples, though a 2025 assessment held that the idea of colonisation as such has been discarded.
The Han dynasty, ruling from 202 BC to 220 AD, used tuntian, self-sustaining agricultural military garrisons, to secure frontier outposts and Silk Road trade routes. Han generals such as Ma Yuan and administrators such as Cao Song extended these colonies into Vietnam, Korea, and the Tarim Basin region of Xinjiang.