The Mad Hatter is a hatter. He makes and sells hats for a living.

Mad as a Hatter was created in 1992.

No. In the original book, the mad hatter doesn't have a name, he isn't even called 'the Mad Hatter', he is simply called 'the Hatter'.

The March Hare is the Mad Hatter's friend.

Only the Mad Hatter is a hatter.

The name "The Mad Hatters Tea Party" might suggest that there is more than one hatter there, but if you put the apostrophe in the correct place it becomes "The Mad Hatter's Tea Party", which means, "the tea party belonging to the Mad Hatter".