They typically move through the solar system in orbits ranging from a few years to several hundred thousand years. Comets are not on fire. As they near the sun, the sun's heat sublimates the comet's ices and releases dust particles which produces the comet's tail. Comets rarely come within a few million miles of Earth and, thus, have a slow apparent motion across our sky.
Typical comets remain visible for periods of several weeks up to several months.
Comets can suddenly brighten or fade from view in a matter of hours. They can lose their tail or develop multiple tails. Sometimes they can even split into two or more pieces, so that, through a telescope, several comets can be seen moving together across the sky. Comets represent some of the oldest, basically untouched objects in the solar system. Their very composition seems to represent the original makeup of the vast nebula that ultimately condensed to form the sun and planets.