Is moyamoya a congenital disease?

YES. Moyamoya disease is generally a congenital disease affecting the arteries of the brain causing them to gradually occlude. Fortunately, collaterals develop to supply blood to critical areas of the brain. These vessels can be frail and are prone to bleeding - which can cause a stroke.
Yes and no. In moyamoya, the inner layer (intima) of the internal carotid artery (ica) overgrows causing blockage of the lumen (opening) of the artery. The icas are two of the 4 major arteries supplying all of the brain. Collaterals form & look like smoke (moyamoya in japanese) on x-ray. Moyamoya can be congenital or acquired. There is also a possible hereditary component on chromosome 17.