Muggles' Guide to Harry Potter/Magic/Goblet of Fire

Overview
The Goblet of Fire is "a large, roughly-hewn wooden cup", "full to the brim with dancing blue-white flames", kept in an ornamental casket.

Extended Description
Professor Dumbledore, in his introduction to the Triwizard Tournament, said that selection of the Champions to represent each school would be done by an "impartial judge". The Goblet of Fire is that judge; those who wish the chance to compete place their names in the Goblet, and at the start time (which is apparently Hallowe'en), the Goblet selects one person from each school by returning one name from each school.

In Harry Potter and the Goblet of Fire, four Champions are selected, apparently giving Hogwarts two shots at the championship. At the time, Professor Moody reminds everyone there that the Goblet is a "powerful magical artifact," far beyond the ability of a fourth-year student to alter, and suggests that the only way that could have happened would be if someone had hoodwinked the Goblet into believing that there were four schools competing, and then entering Harry's name as the sole competitor from this fictional fourth school. Karkaroff, the Headmaster of Durmstrang, demands that the names be re-submitted, but is told that the Goblet has extinguished itself and will not re-ignite until it is time for the next Tournament.

Questions

 * 1) During the hiatus in the Triwizard Tournament, did the Goblet ignite every five years and wait, flaming patiently, for submissions?
 * 2) Where is the Goblet now?