1) Wilhelm Wundt is the first person to segregate out psychology as a specific part of philosophy and actively conduct experimental research in psychology in a way we would recognize today. A U.S. follower of his, William James, is often seen as the first thinker to conceive of psychology as a field of science that includes the full range of what we currently consider in psychology. He pretty much set the boundaries of what we now call psychology in is book "The Principles of Psychology".
Before these two, various predecessors had discovered pieces, or focussed on individual theories that we now consider psychological (From Aquinas (or even Aristotle) to Pavlov). But they had no collected view of how physiology, mental models and behavior fit together into a single subject.
2) Although it has many scientific tools, anthropology accepts a different view of science, and will never move toward integration with the other modern sciences. Historiography can never be scientific, as stories always have tellers, and the results always contain relativised perspectives that cannot be otherwise captured and contained. Sociology logically precedes psychology. Although it remains a weaker science, it is slightly older. It was mature enough to generate 'Suicide' (sometimes considered its first work) at a point where psychology was still coming together.
One could claim that modern Linguistics is the latest new science, the Chomsky school pulled a critical mass of it away from the anthropological model and into a framework that generates more testable hypotheses. And Chomsky is still alive. But maybe folks are thinking that while its progenitor is still alive, such a change may not be permanent.
3) Despite a lot of failures to converge, and a tendency to back away from the challenges of paradigmatic consistency, psychology has already had fairly long periods of modern science, where work in various schools proceeded within a logical paradigm, and were fully accepted by all the other schools. One can see the ascendency of Behaviorism as such a period. So I think by Kuhnian standards, this is an established science, just one prone to a lot of weak paradigms and pointless revolutions that circle around and undermine progress.