Short answers, pulled from the story.
Oceanus was the eldest of the Titans, born to Uranus, the Sky, and Gaia, the Earth. Hesiod lists his siblings as Coeus, Crius, Hyperion, Iapetus, Theia, Rhea, Themis, Mnemosyne, Phoebe, Tethys, and Cronus.
Oceanus married his own sister, the Titaness Tethys. Hesiod counts three thousand river-god sons and three thousand Oceanid daughters born to the couple.
No, according to most sources Oceanus stayed out of both conflicts. The mythographer Apollodorus says every Titan except Oceanus attacked Uranus, and Oceanus also avoided the Titanomachy against Zeus, though he sent his daughter Styx and her children to fight on Zeus's side.
The origin of the name Oceanus is obscure and cannot be explained from Greek, according to M. L. West. Several scholars propose a Semitic origin, R. S. P. Beekes suggests a Pre-Greek Aegean loanword, and Michael Janda argues for possible Indo-European roots.
Oceanus appears with bull horns, a snake, and a fish on the early sixth-century BC "Erskine" dinos by Sophilos, and on the similar François Vase. On the second-century BC Pergamon Altar he fights Giants, and in Hellenistic and Roman mosaics he is shown as a bearded man with crab-claw horns and a serpent's lower body.
The Greeks pictured Oceanus as the river encircling the entire earth, the source of all rivers, seas, springs, and wells according to Homer. Later writers identified him with the Atlantic Ocean, and some late traditions equated him with the Black Sea.