In colloquial use a “myth” is something that’s false but often accepted as true. But this is quite separate from the original meaning, a sacred story.
Regarding the examples you gave, whether they are myths or not has nothing to do with whether the beings or extraordinary events actually happened. Stories that are entirely earth-bound (if you like) can be myths, although it is true that extraordinary elements are usually found in there to signify that the events transcend normal space and time. What makes something a myth, rather, is that it is a story that conveys a sense of transcendent or unifying meaning especially within a community.
In this sense, if we were to remove all the so-called “supernatural” elements from the Buddha’s life, it would still be a myth (and still embody the stages of the classic hero myth). Miracles and magic just make it more fun, like CGI in a movie. But it doesn’t change the meaning of the myth. As opposed to, say, the story of Jesus, where the resurrection is essential to the myth.
As for the specifics, some of the things you mention are elements within a mythic story, such as point 3. The miraculous birth is an essential element in the hero myth.
The Mahayana claims make up what I regard as a sectarian mythology. I discussed this in my Sects & Sectarianism, although mostly in the context of the early schools rather than Mahayana. They’re essentially a form of early propaganda, stories invented as marketing, which consciously assume the form and motifs of classical mythology in order to convey authority to their school. None of them are true, if that is what you’re asking.
But this is, and I hope you pardon me for this, all trivial. None of it gets to the heart of the matter, which, why does myth matter? What is the hold that such stories have over us?
True myth goes back to a deeper place in consciousness and in human society. It is not consciously formed, it evolves and grows. Myths are stories that are told and retold for centuries, millenia, until they lose the sense of one person’s story, and become universal. They don’t consciously set out to be anything, they grow into their own meaning. Because their origins are lost in time, they are never heard for the first time; they are part of a fabric of culture, always there, permeating it in story, ritual, image, embedded in the foundations of language.
Tolkein knew this, which is why he began by creating language, then found stories to tell in those languages. Why is it that when people see something like Aragorn being made king, it’s such an emotional and powerful moment: but we believe in democracy? Myth is contacting something deeper, more primal than we can reach with our rational mind.
The essential form of myth is the origin story. To the beginning: that is where all myths lead. Now, in part, they do this because, as stories told and retold through countless generations, they do in fact preserve accurate information about the past. But on a deeper level, they tell of a primeval past that is still alive today. As stories, they keep the past alive; and the very fact that they are still told tells us that they still mean something for us today. The present repeats the patterns and problems of the past; mythic time is cyclic time, which is why the myths “never were, but always are”.
If the essential form of myth is the origin story, the essential theme is the death of god. Consider the Bible. We are used to thinking of it as the story of Gods word’s and actions. But if you step back from it, God was right there “in the beginning”. But with every step of the way, he recedes further form the action. He stays behind in the Garden. Soon he can only be seen in the stormy clouds or in a passing shadow, or in bizarre and twisted forms. Then he can’t be seen at all: he must send his son. Who in turn leaves, and, breaking his promise, doesn’t come back. Now all we have is a dried up piece of bread. The Bible is the story of the death of God.
But this is just one example. In Egypt, Greece, India, Persia, everywhere we see the same thing. And not only that, we see the same thing right from the very beginning. The very oldest myth we have—Gilgamesh—already contains recollections of older myths, and reflections about the betrayal and withdrawal of the gods.
This is, of course, an overriding theme of the Buddhist texts. While they are typically more gentle in their approach—we don’t nail our old gods to crosses, we tell jokes about them—the effect is the same. Once you have enough distance and irony to be able to tell a joke at god’s expense, that god is over. We no longer rely on divine intervention and revelation for truth or meaning, we rely on our own experience, reason, and awareness.
The story of the death of god is also the story of the ascent of humanity. Nietzsche:
God is dead. God remains dead. And we have killed him. How shall we comfort ourselves, the murderers of all murderers? What was holiest and mightiest of all that the world has yet owned has bled to death under our knives: who will wipe this blood off us? What water is there for us to clean ourselves? What festivals of atonement, what sacred games shall we have to invent? Is not the greatness of this deed too great for us? Must we ourselves not become gods simply to appear worthy of it?
The death of god is no modern invention. Buddhists have been killing gods for 2,500 years. But we were not alone: the axial age spelled the ending of true myth. Or to put it another way. In order to create the great myths, a society needs a certain degree of development: sufficient size, trade interactions, wealth, stability, and a specialized, leisured class of literati. But the same factors that make this possible are also the factors that bring to a close the era that the stories tell of. Thus myth, in the form that we have it, tells the story of its own death. This is the birth of self-reflection: a story about its own story.
The story of the Buddha, while cast in the form of myth, is no longer an organic growth over centuries. It is a conscious, deliberate formulation, conceived by masters of literary structure. And, crucially, it is not the core of the thing; what matters is the Dhamma, not the Buddha’s life.
One of the few modern masters of myth, Roberto Calasso, summed it up perfectly: the Buddha came to put an end to gesture. No longer was spiritual life measured by external expressions of narrative, sign, and ritual, but by an inner awakening.
Buddhism—together with the other rationalizing movements of the time like Jainism—was the first generation of of post-mythic religions, serving a similar role as the philosophers did in Greece. From then on, myth was used as a storytelling device, just as Hollywood uses it today. It might be used by people with a greater or lesser grasp of its depths, in more or less powerful or profound ways, but it is being used, deliberately, rather than emerging organically from the depths. Something like the Buddhacarita is as much a precursor of the modern novel as it is the inheritor of the ancient myth.
This is not to say that myth is in fact dead in Buddhism; there is always a vast gap between the insights of the sages and the understanding of the masses. When Thai boys relive the Buddha’s renunciation through the ordination ritual, this has nothing to do with a search for inner awareness, and everything to do with a ritual embodiment of myth. Myth is very much alive for many Buddhists; and the unawareness of this fact underlies many of the tensions we find in modern Buddhism.
I have argued many times that the denial of myth, the chronic lack of understanding of what it is and why it matters, pervades modern Buddhist study and practice. You’ll learn more about myth by going to see Star Wars than you will by reading anything written by modern Buddhist academics on the subject. We have what is probably the largest and oldest collections of sacred stories anywhere in the world, yet they are routinely ignored and dismissed.
This is one of the reasons I abandoned my plan to write a proper article on Buddhist mythology for Wikipedia. The current article is appalling, but it is an reasonable representation of the current state of awareness and study of the issue. Wikipedia relies on citations, and on most issues there simply aren’t any.
There are many rich veins of insight and study of myth in modern times. It would be nice to see the current impoverished study of Buddhism tap into these.