Short answers, pulled from the story.
Neptunalia was held on July 23rd, during the peak of summer heat when freshwater sources were at their lowest. Romans built shelters from tree branches in a woods between the Tiber and the Via Salaria, drank spring water and wine, and offered a bull sacrifice to Neptune. The festival was one of three consecutive summer celebrations connected to water and drought.
The etymology of Neptunus is disputed. Georges Dumézil connected it to the Indo-European root nepots ("descendant"), linking it to the Indian Apam Napat, the Avestan Apam Napa, and the Old Irish Nechtan, all meaning "descendant of the waters". Other scholars proposed derivations from roots meaning "moist substance" or from the Etruscan toponym Nepe or Nepete, the town now known as Nepi near Falerii.
Neptune's only temple in Rome stood near the Circus Flaminius in the southern Campus Martius and dated back to at least 206 BC. The consul Gnaeus Domitius Ahenobarbus restored it around 40 BC, an event commemorated on a coin. Inside was a sculpture of a marine group by Scopas Minor.
Salacia and Venilia were Neptune's paredrae, entities representing the fundamental aspects of his power. Varro connected Salacia to salum (the sea) and Venilia to ventus (wind). Dumézil interpreted Salacia as representing the violent, gushing aspects of water and Venilia as the tranquil, still or slowly-flowing waters.
The Etruscan name for Neptune is Nethuns. It appears twice on the Liver of Piacenza (on section seven's outer rim and on section 28's gallbladder) and eight times across columns VII, IX, and XI of the Liber Linteus. A bronze mirror from Tuscania dated to 350 BC in the Vatican Museums depicts Nethuns holding a double-ended trident and conversing with the sun god Usil and the dawn goddess Thesan.
Neptune's association with horses came through his identification with the Roman deity Consus, whose underground altar in the Circus Maximus was the site of horse races on the summer Consualia (August 21st). Consus was later reinterpreted as Neptunus equestris under the influence of the Greek Poseidon Hippios. Martianus Capella placed Neptune and Consus together in region X of heaven.