Sources--his biographies (there are numerous good ones). His speeches. His sermons. His books. His autobiography. The King papers. The papers housed at the LBJ library that discuss him (he was the subject of much government investigation, as you can well imagine). The King Center. See the links I posted above. It's about as easy to separate Christ from King as it is to separate Christ from the Gospels.
One of many sources from the King papers
Originally Posted by King quote
At present I still feel the affects of the noble moral and ethical ideals that I grew up under. They have been real and precious to me, and even in moments of theological doubt I could never turn away from them. Even though I have never had an abrupt conversion experience, religion has been real to me and closely knitted to life. In fact the two cannot be separated; religion for me is life.
Your "source" on Gandhi and King--lovely feel-good article by a former Indian Ambassador-turned-journalist (no bias there of course), not scholarly at all. There is no documentation for the quotes listed.
Anyone who wants a _good_ history of King should look up any of the many scholarly historical books written about him, and cross-reference it with his speeches and the documents housed at the King Center, Stanford, and LBJ Library.