In what way can the study of the origins of philosophy in the pre-socratic thinkers illuminate the nature of philosophy?
Oh, yes, it is certainly worthwhile for anyone interested in philosophy. While the term "pre-socratic" is arbitrary it is a useful marker for grouping a milieux of intellectual ferment and abstract theorizing usually dated from Thales up to Parmenides, say.
Sources for these thinkers are scarce and reading the fragments of someone like Heraclitus or Parmenides first hand can be a little baffling, rife with rather mystical and allusive claims. But the general take is that Ionian philosophy before Socrates was more like proto-physics, driven by attempts to explain natural phenomena without recourse to gods and traditions.
Starting with Thales, arguments centered around the reduction of all substances to a single substance or mode, whether water, fire, aether, numbers, atoms, or whatever. This is, as many have noted, the basic framework of what modern physics attempts to do under such terms as energy or matter. At the same time, the pre-socratic Sophists analyzed customs, laws, norms, and forms of argument from a naturalistic skeptical standpoints, and might be called photo-sociologists.
Socrates marked a turn from such naturalistic approaches to a concern with morals, truth, the sources of knowledge, metaphysics... in short, idealism. For some philosophers, such as Heidegger and some physicists, this Socratic turn actually set philosophy muddling down the wrong path.
But for those who admire Socrates and Plato, as I do, probably the best reason study the pre-socratics is to understand Socrates and what he was, in part, arguing against or striving to overcome. While rhetoricians and poets were his chief target, Sophists and other working philosophers get thoroughly laundered in the dialogues. I'm jumbling together and over-simplifying a lot here, but my basic answer is: yes, illuminating on many levels.
Yes. It's interesting and useful, in terms of anthropology and understanding human development and cultural variation.
David Graeber argued in Debt: The First 5000 Years that the 'universal substances' of presocratics can be linked to the emergence of currency, and the idea of 'universal' store of value.
There is the Needham Question, about why China invented paper, gunpowder, canals & magnetic compasses, called 'cornerstones of the modern era', yet the modern era did not begin there. While accepted as having a lot to do with geography, ideas of natural laws that originated with the presocratics are also in the mix.
I'd argue the Pythagorean 'math cult', along with Socratic dialogue, are the crucial components of the Academy, and so of academia, arguably the dominant culture of knowledge now. Mathematical Platonism is still widespread, and still, a math cult.
Incidentally, I'd argue Socrates defined the role of philosopher, and the meaning of philosophy, discussed here: What is the difference between western and other philosophies? Undoubtedly other people and cultures before him pursued truth, but Socrates gave a distinctive form to what philosophy is, and identifying it before that is done retrospectively, post hoc, and we should be wary applying the term earlier because of that. Imho.