As to the question of Keynesians being socialist, or not, I might call him a technocratic socialist, to distinguish his position from the labor socialism of Marx and his successors. Keynes argued that "a somewhat comprehensive socialization of investment" was sufficient to bring about full employment and maximum (or desired) productivity and offered methods for achieving that using existing financial and governmental structures. The goals he set out, I would say, were socialist, in the sense of governing the economy for the welfare of all, rather than a ruling class, but his methods were entirely different from those proposed by socialist parties, and in contradiction to those of communism. Rather than the minute planning of every aspect of the economy, which was popular among some socialists of his day, he proposed to eschew minute planning and instead govern investment in a way favorable to a broad middle class. He set out ways in which a democracy might accomplish goals of economic fairness without overturning the whole of society.
Because of this, socialist and communist parties opposed his ideas and, so far as I know, still do. The whole labor socialist project is called into question by Keynesian economics. Because of his advocacy of control of investment, he also has strong opposition on the part of the right, from the wealthy who do not wish to give up even partial control of their wealth and also from people who prefer an aristocratic social order.
And all of this is very much a shame, because it is not like labor activism would be unnecessary in an polity governed by Keynesian precepts, nor would leaders and rulers become unnecessary in such a society. If the various factions would see past their ideologies, Keynesianism has much to offer both sides. In such a society, labor need not fear impoverishment from arbitrary financial policies or random economic weather and rulers and leaders need not be authoritarians.