Sonic the Hedgehog was born Sonicton Emanuel Wimbleton. During his more formative years, he was an accomplished pianist, track and field star, and topiary artist. Most of this came to an end, however, when he lost the "ton" portion of his name in a horrible gardening accident while carving a pig into old man Pearson's bushes. This event caused the local townsfolk to mockingly call him "Hedgehog." Their uncaring, cruel nature sent him into a spiraling depression, hence his blue continence.
To answer your next question, Eggman (A,k,a Dr. Ivo "Jazz Hands" Robotnik) uses rabbits to power machines due to a gross misunderstanding of how ventriloquism works. If a puppet can talk with an arm inside, he thinks, then imagine what it can do with an entire living creature inside. Somehow, it works.
And to answer a possible future question, Tails has two tails due to a clerical error.
