Short answers, pulled from the story.
Dacia was an ancient kingdom whose core lay in Transylvania, stretching west to the river Tisza, east to the Black Sea, and south to the Danube. It roughly corresponds to present-day Romania along with parts of Moldova, Bulgaria, Serbia, Hungary, Slovakia, the Czech Republic, Poland, and Ukraine. The Carpathian Mountains ran through its center.
Burebista ruled the Geto-Dacian tribes from 82 BC to 44 BC and united them into a kingdom at its greatest extent. He conquered the Bastarnae and Boii, gained authority over Greek Black Sea cities including Olbia and Apollonia, reorganized the army, and moved the capital to Sarmizegetusa Regia. He was murdered in 44 BC, the same year as Julius Caesar, and the kingdom immediately split into four parts.
Emperor Trajan conducted two campaigns against Dacia, first in AD 101-102 and then again in AD 105-106. The second campaign ended with the Siege of Sarmizegethusa, the razing of the Dacian capital, and the suicide of King Decebalus to avoid capture. Trajan built the Column of Trajan in Rome to commemorate the victory and organized the conquered territory as the Roman province Dacia Traiana.
The suffix dava meant settlement or village in the Dacian language. Ptolemy listed 43 town names in Dacia, of which arguably 33 were of Dacian origin, and most carried this suffix. Examples within Dacia include Acidava, Buridava, Cumidava, Ziridava, and Singidava. The same naming pattern appeared in towns Ptolemy recorded across Lower Moesia and in the Upper Vistula basin in what is now southern Poland.
Decebalus ruled the Dacians between AD 87 and 106. His name translates as "strong as ten men." He initially defeated the Roman general Cornelius Fuscus in AD 87, secured client-king status with payments from Rome after the Battle of Tapae in AD 88, then rebuilt his power and attacked Roman garrisons again in AD 105. When Trajan's forces sacked Sarmizegethusa during the second campaign, Decebalus committed suicide to avoid being taken captive.
Emperor Aurelian withdrew Roman troops from Dacia between AD 271 and 275. According to the historian Eutropius, Roman citizens from the towns and lands of Dacia were resettled to the interior of Moesia. The province had been established after Trajan's conquest in AD 106 and was known as Dacia Traiana and later Dacia Felix.