Where did the first maze garden originate and what was its purpose?

Answer 1

Don't know if a specific one can be pinpointed as the first. From Garden History Info:

"Many European countries have turf and stone labyrinths cut into hillsides that are thousands of years old, and even Shakespeare mentions that 'treading the maze' was a well-established folk custom in England."

As to the purpose, from the same site:

"As in cathedrals, so also in medieval gardens, although the symbolism in secular gardens was not so high-minded as that within the cathedrals. There has long been conjecture that one of the most important ideas associated with labyrinths is that of fertility (this somewhat allied with the idea of spiritual rebirth that the Church promoted); the long winding canal of the unicursal labyrinth, the emergence from the dark heart into the light of day, clearly has connotations with giving birth. May-pole dances reflect the labyrinth and the unwinding into life and birth again — May dances being not only danced versions of the labyrinth, but also a spring rite. "

Check the link below for the full history. Have fun!

Answer 2

You might want to check out places like aroboretums and botanical gardens to answer those questions.