Short answers, pulled from the story.
Giovanni Domenico Cassini discovered the moon Dione in 1684 while searching for moons around Saturn. He set up a large aerial telescope on the grounds of the Paris Observatory to make this finding.
John Herschel suggested using names from Greek mythology for all Saturnian moons in 1847. William Lassell reported this naming convention in Monthly Notices of the Royal Astronomical Society on the 14th of January 1848.
Dione completes one orbit for every two orbits completed by Enceladus. This 1:2 mean-motion orbital resonance maintains Enceladus's orbital eccentricity at 0.0047.
A water ice envelope surrounds the rocky core with a thickness of about 160 km. Models suggest the lowermost part of this layer could be liquid salt water.
Cassini flybys on the 13th of December 2004 proved these wisps were actually ice cliffs created by tectonic fractures called chasmata. Some cliffs reach several hundred meters in height according to oblique images taken on the 11th of October 2005.
Molecular oxygen ions form the primary component of this exosphere around Dione. Instruments aboard Cassini detected these ions on the 7th of April 2010 with a density ranging from 0.01 to 0.09 per cubic centimeter.