Zodiac is Night and Air
Metal is Water and Light
Mythic is Fire and Air
Cosmic is Magic and Air
Gemstone is Water and Forest (can also be crafted)
Dino is Fire and Forest
Stone is Light and Forest
Rainbow is Water and Air
Fairytale is Forest and Air
Tropic is Water and Fire
Royal is Magic and Air
Treasure can only be bought with gold
Champion can only be won from tournaments or crafted from parts won in battles
Not sure about Olympus, got mine from a World Event ( another cool new feature ) but I think it may be breedable.
Of course you needn't use the pure types, Fairy and Fruitful can give Fairytale. And so on.
Oh and welcome back to the game!