Short answers, pulled from the story.
The Roman era of Greek history began in 146 BC with the Roman defeat of Corinth at the Battle of Corinth. This followed the Fourth Macedonian War, which ended in 148 BC, and marked the start of Roman control over the Greek peninsula.
Greece served as a major crossroads of maritime trade between Rome and the Greek-speaking eastern half of the empire. Rome established Corinth as the capital of the province of Achaea, and Athens functioned as a cultural hub of philosophy and education. The Greek language became a lingua franca across the eastern provinces and was used by educated Romans.
Treatment varied. Cities such as Athens and Sparta retained the status of free cities, with partial autonomy and exemption from direct Roman taxation. Rome transferred political power toward propertied classes, dissolved the leagues between cities, and restricted direct trade, but confiscated little land and levied a land tax rather than imposing harsher terms.
Hadrian built the Library of Hadrian in Athens and completed the Temple of Olympian Zeus, a project abandoned roughly 638 years earlier. Before becoming emperor he had served as the eponymous archon of Athens, and the Athenians built the Arch of Hadrian in his honor.
Recent archaeological discoveries support a picture of broad prosperity in late antique Greece. The text known as Hierocles' Syndekmos records approximately eighty cities and a highly urbanized landscape. Scholars now widely accept that between the 4th and 7th centuries AD, Greece was one of the most economically active regions in the eastern Mediterranean.
After the death of Theodosius I in 395 AD, the Roman Empire split into western and eastern halves. Greece remained part of the Eastern Roman Empire, later called the Byzantine Empire. Emperor Heraclius changed the empire's official language from Latin to Greek in the early 7th century, formalizing the Hellenization that had long characterized the eastern provinces.