Short answers, pulled from the story.
Valerian was proclaimed emperor by Raetian soldiers in 253 after Trebonianus Gallus was killed by his own troops during a rebellion led by Aemilianus. When Valerian reached Rome in September, Aemilianus's legions defected and killed him, and the Senate quickly acknowledged Valerian as emperor.
Valerian was captured by the Persian emperor Shapur I after the Battle of Edessa, probably in June of 260, becoming the first Roman emperor ever taken prisoner in battle. The defeat caused shock and instability throughout the Roman Empire.
Accounts differ. The Christian writer Lactantius claimed Valerian was humiliated, used as a human footstool, and later killed by being forced to swallow molten gold or flayed alive, with his skin stuffed and displayed as a trophy. The modern scholar Touraj Daryaee argues instead that Shapur settled Valerian and his soldiers at Bishapur or Gundishapur in relatively good conditions.
Yes. Valerian sent two letters to the Senate, in 257 and 258, ordering Christian clergy and leaders to sacrifice to the Roman gods or face punishment, including execution, banishment, loss of property, and enslavement. His son Gallienus rescinded the decree upon becoming emperor in 260.
Valerian's son Gallienus, whom he had appointed co-emperor at the start of his reign, continued ruling after Valerian's capture in 260. Gallienus held the throne despite repeated threats from usurpers until his own assassination in 268.
Stone carvings at Naghshe-Rostam in Iran depict Valerian holding hands with Shapur I, a gesture read as a sign of submission.