Short answers, pulled from the story.
The Cassini Imaging Science Team identified Polydeuces in images taken on the 21st of October 2004. The International Astronomical Union announced the discovery on the 8th of November 2004.
The International Astronomical Union officially named the moon Polydeuces and assigned it the designation Saturn XXXIV in early 2005. The name was approved and announced by the IAU Working Group on Planetary System Nomenclature on the 21st of January 2005.
Polydeuces follows a tadpole orbit around Dione's trailing Lagrange point with significant oscillations caused by gravitational perturbations from other moons. Its angular distance behind Dione oscillates from 33.9 degrees to 91.4 degrees over a period that spans several years.
Dynamical modeling suggests Tethys and Dione started with similar amounts of material for trojan moons to form with roughly similar sizes. However, Helene and Polydeuces differ significantly in mass by more than an order of magnitude and this mass asymmetry remains unexplained despite extensive study of their origins.
The most recent estimate for Polydeuces's dimensions as of 2015 corresponds to a volume-equivalent mean diameter of about 3 kilometers. Cassini imagery reveals an elongated shape and a smooth surface coated in fine water ice particles derived from Enceladus's cryovolcanic plumes.
Cassini's closest encounter with Polydeuces took place on the 17th of February 2005 when it passed within 480 kilometers while moving outbound from periapse. Resolved images were captured only on the 22nd of May 2006, the 10th of May 2015, and the 16th of June 2015.