Is what you see of the maze the whole thing or will more of it pop up after you clear all the chests and dragons?

First, please post in the appropriate area in order to keep the forum organized. Second as to your question, the entire map should be visible. However obtaining all three dragons for free is not possible, if you want the first two for free I suggest you do not do any moving and wait for maps to show up with the cheapest and best paths.