"A unicorn (from Latin unus 'one' and cornu 'horn') is a mythological creature. Though the modern popular image of the unicorn is sometimes that of a horse differing only in the horn on its forehead, the traditional unicorn also has a billy-goat beard, a lion's tail, and cloven hooves—these distinguish it from a horse. Marianna Mayer has observed (The Unicorn and the Lake), "The unicorn is the only fabulous beast that does not seem to have been conceived out of human fears. In even the earliest references he is fierce yet good, selfless yet solitary, but always mysteriously beautiful. He could be captured only by unfair means, and his single horn was said to neutralize poison." " "Alleged evidence Otto Von Guericke's unicorn skeleton, exhibit near the Zoo, Osnabrück Among numerous finds of prehistoric bones found at Einhornhöhle (Unicorn Cave) in Germany's Harz Mountains, some were selected and reconstructed by the mayor of Magdeburg, Otto Von Guericke, as a unicorn in 1663 (illustration, right). Guericke's so-called unicorn had only two legs, and was constructed from fossil bones of a Woolly rhinoceros and a mammoth, with the horn of a narwhal. The skeleton was examined by Gottfried Leibniz, who had previously doubted the existence of the unicorn, but was convinced by it. Baron Georges Cuvier maintained that as the unicorn was cloven-hoofed it must therefore have a cloven skull (making the growth of a single horn impossible); to disprove this, Dr. W. Franklin Dove, a University of Maine professor, artificially fused the horn buds of a calf together, creating a one-horned bull. P. T. Barnum once exhibited a unicorn skeleton, which was exposed as a hoax. Since the rhinoceros is the only known extant land animal to possess a single horn, it has often been supposed that the unicorn legend originated from encounters between Europeans and rhinoceroses. The Woolly Rhinoceros would have been quite familiar to ice age people, or the legend may have been based on the rhinoceroses of Africa. Europeans and West Asians have visited Sub-Saharan Africa for as long as we have records. Unicorn seals of the Indus Valley Civilization The first objects unearthed from Harappa and Mohenjo-Daro were small stone seals inscribed with elegant depictions of animals, including a unicorn-like figure in upper left, and marked with Indus script writing which still baffles scholars. These seals are dated back to 2500 B. C. Source: North Park University, Chicago, Illinois.(Image : A Harappa Seals.) This seal is a close-up of the unicorn-like animal found in Mohenjo-daro, measures 29mm (1.14 inches) on each side and is made of heated Steatite. "Steatite is an easily carved soft stone that becomes hard after firing. On the top are four pictographs of an as yet undeciphered Indus script, one of the first writing systems in history." Image source Dept. of Archaeology and Museums, Govt. of Pakistan.(Image : A Harappa Unicorn." "2 Origins 2.1 Alleged evidence 2.2 Unicorn seals of the Indus Valley Civilization 2.3 Elasmotherium or rhinoceros 2.4 A single-horned goat 2.5 The narwhal 2.6 The oryx 2.7 The eland 2.8 Genetic disorders of horned animals" Source and further information: http://en.wikipedia.org/wiki/Unicorn

No.

Just as much as Jesus exists. Anything can exist in the imagination. :-)

shortly answered: no.

I think the keyword here is 'mythological'. :o)

Possibly. Supposedly, over 99.9% of the creatures that ever existed on earth are extinct. There are surely not fossil remainders of all these species. Many mammals have horns. It wouldn't be beyond the realm of possibility to have a horselike creature with a horn.

there are many unexplained things in this world. i like to keep my mind open to every possibility. so maybe they did at one point

Nope. :-)