Pompeia Plotina Claudia Phoebe Piso (d.121/122 AD) was the wife of the Emperor Trajan, and noted for her interest in Epicurean philosophy. Her relationship with Hadrian was clearly a close one: Cassius Dio claims that she was in love with him (although there is no suggestion of any physical impropriety between them), and the Historia Augusta hints that she may have forged Trajan's will to ensure Hadrian's succession. After her death Hadrian secured her deification and built a temple to her in Nimes.
This refers to Trajan's last military campaign in Mesopotamia, which was ultimately unsuccessful. It is unclear whether his motives were territorial (there are some suggestions that he even intended to imitate Alexander the Great) or economic (control of the trade routes to India, which supplied many of the spices essential to Roman cuisine). Hadrian later took the decision to abandon these conquests altogether.
A literal translation of the phrase could be "global stability" or "regional stability" and, as such, it could refer to Hadrian's policy of consolidating the existing borders of the Empire, in contrast to the Trajanic policy of further conquest.
A more specific meaning is also intended here, however. "Tellus" is a goddess of the Earth, a Roman equivalent of the Greek Gaia, and "Tellus Stabilita" is thus the genius of the "Pacified Earth," sometimes depicted in Roman imagery.
Opramoas was a wealthy individual from Rhodiopolis in Asia Minor (modern Turkey). He was a proponent of "euergetism," a Pagan Hellenistic and Roman form of philanthropy. Inscriptions from his mausoleum state that he donated money for the education of children, for the burial of the poor and for the dowries of girls from poor families. Clearly he was a man of substantial wealth, and it is likely that he was involved in trade between Asia and the Roman Empire, so he would have been well-placed to play the role ascribed to him here, although there is no evidence that he actually did so.
Osroes I of Parthia (reigned 109-129 AD) was a prince of Graeco-Iranian ancestry. His invasion of Armenia had prompted the war with Trajan. Following Trajan's death, however, Osroes displaced Parthamaspates, the vassal installed by Trajan, to reclame the Persian throne. Hadrian acknowledged this as a fait accompli, and returned his daughter, taken as a hostage by Trajan.