The map is featured in this book:
A Tolkien Bestiary in black and white. I'm not sure who made the map though (not the writer, probably) and I'm not sure if it's featured in another book too.
On the topic of Arda: at first, Arda was indeed flat. When Melkor was defeated Illuvatar "bend" the world, widely believed to be meaning that he made Arda into a sphere.
A lot of different maps are floating around on the internet that are said to depict the whole continent of Middle-earth. I believe Tolkien only ever drew a couple of rough maps. The standard map (see below) was drawn by his son and approved by the Professor. I believe that beyond this map, pretty much nothing is known. Some hints are given (the Dark Lands, the Eastern Sea etc), but none of these were featured in any canonical maps. That is why people across the world have made them for their purposes. The map you posted is probably one of these, with a lot of canonical accuracy. Some parts though, are I believe still filled in by the artist himself and not based on Tolkien's sketches.
The book "the Atlas of Middle-earth" contains a lot fo maps which are very accurate for the biggest part. I've also posted some below.
Map of North-Western Middle-earth:
Arda in the First Age:
Middle-earth in the Second Age and on (first image):
http://www.tolkienforums.com/thirdagemaps.htm