Turns out there's actually zero lore relating to my questions for a race that's been around since, what, 2e?
Githyanki and githzerai were introduced in the 1981 Fiend Folio, with a cover illustration of a githyanki, and a full-page interior drawing of a battle between githyanki and a party of adventurers. In 1996, the Planescape accessory A Guide to the Astral Planes appeared, and it contains what must be the longest treatment of githyanki in any AD&D product:
In a time before most of the prime worlds known today were born, when the gate-towns of the Outlands all went by different names, when beings could recall days before the creation of then-bejeweled Sigil still existed, the illithids held an ancient empire. This great empire stretched throughout many prime worlds, infested both Astral and Ethereal, and threatened the borders of many of the Outer Planes. The mind flayer dominion was so powerful that vast planar armies marshaled to defend their respective realms. Even the fiends paused in their eternal Blood War long enough to determine if the illithids would attack the Lower Planes as well. Despite the fact that most tomes of historical lore make no mention of it (for truly ancient was this time, and older still the roots of the illithid empire), never has there been a time since then when the entire multiverse has been so vexed by a single threat.
Salvation came not from without, but rather within. The illithids had enslaved all of the humans that they had come upon and (as they are still wont to do) used them as beasts of burden and livestock upon which to feed. These slaves were without number, and many were actually descendants of those who had originally been conquered, so that they knew no life beyond mind flayer enslavement, nor did their parents, nor indeed even their parents before them. Slavery and other unspeakable influences of the illithids twisted these wretches in form as well as spirit, but many still clung to the ever-present need for freedom.
Slave revolts clawed at the illithid empire, but never posed a true threat. What hope did poorly armed, malnourished slaves have against the awesome mental powers of their illithid masters? The slaves knew that only through the development of their own psionic powers, coupled with martial strength, would they ever emerge victorious. From their number arose a champion, greater in mental strength and resolve (and most likely hatred) than her peers. Her name was Gith. With her leadership at its crest, the wave of slaves washed over the illithid empire without mercy. Fueled by her power and rage, the rebellion tore asunder the mind flayer's dominion, casting the shreds to the wind. Not every illithid was killed, and not every stronghold fell (as was Gith's wish), but the ties of the empire were broken, and the defeat was one from which the mind flayers would never completely recover. The slaves were freed, most tasting the sweet nectar of liberty for the first time.
At this point, when Gith ordered her people to continue their campaign to annihilate the illithids and establish an empire of conquest of their own, not all followed her command. A new figure, by the name of Zerthimon, had gained a significant following and challenged Gith‘s plans and her leadership. Gith was evil, the newcomer claimed, and would lead the people into darkness and tyranny not unlike the illithids themselves. Thus, no sooner had the people finished their war for freedom than they engaged in a bitter and bloody civil war. In the ensuing conflict, Zerthimon was killed and his followers, now called githzerai, retreated to Limbo in defeat. The losses that Gith’s forces had sustained, however, were too severe for them to press forward in further conquest. Gith led her people, who now called themselves githyanki, “the children of Gith,” to the conquered illithid settlements on the Astral Plane. There, she believed, they would be safest until such time as they could once again begin their conquest of the multiverse, as well as the eradication of the illithids and the githzerai.
Soon after the githyanki had established themselves in the virtually lifeless Astral, a wizardess named Vlaakith began advising Gith in matters of state. She advised the ruler that the githyanki were in need of allies, and Gith reluctantly agreed. After a failed attempt to gain the slaadi, Limbo’s native race, as allies against the githzerai, Vlaakith advised Gith to descend into Baator to meet with the legendary Tiamat. What actually occurred at that meeting is one of the best-kept secrets in all the planes. Simply put, no one knows but Gith, Tiamat, and apparently one of Tiamat’s consorts, a red great wyrm named Ephelomon. What is known is that Ephelomon came to the Astral and instructed Vlaakith that Gith had named the wizardess as the githyanki leader’s successor,
and that she was to carry on her legacy of conquest, for Gith would not be returning. The great wyrm also announced that an eternal pact between red dragons and the githyanki was now in place.
Ephelomon’s words proved true, as the githyanki found when they traveled to the Prime Material. Whenever the githyanki arrived on the Prime, red dragons were willing to work with them in their schemes and goals. Vlaakith and her descendants have always ruled the githyanki since then, but they have slowly lost the resolve and focus of Gith. The githyanki have become fragmented, forming small isolated groups rather than maintaining a single, unified nation. Although no conflict exists between the groups, and they all ultimately serve the queen, each has its own separate goals.
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The githyanki resemble the humans that they descended from in the most basic ways only. While still humanoid, their rough, leathery skin is pale yellow, and their features are gaunt in the extreme. Fact is, some githyanki could be described as skeletal in appearance. Their black eyes have sunk far back into their long, angular skulls, and their noses’ve receded to become very small and highly placed, giving their entire face the appearance of having been stretched vertically. Raven-black or fire-red hair adorns
their heads and is usually worn to reveal their pronounced, pointed ears which are often marked by ridges gained in dark ceremonies.
The dark of it is that while they were illithid slaves, the githyanki (and githzerai) underwent horrible experiments by their masters in an attempt to make them great warriors for the mind flayer empire. They were also forced to work in areas no human was ever meant to be, where strange energies altered them for all time. Lastly, those who would one day become githyanki altered themselves with their own incredible resolve and hatred, twisting themselves in mind,body, and spirit.
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The most pronounced deviation of the githyanki from their human origins is that they have become egg-layers.
This is either the result of some experiment of the illithids or the exposure to some strange astral energies. In either case, this method of reproduction closely resembles that of reptilian creatures. Within githyanki communities, there is always an egg chamber (or possibly many of them), where all eggs are kept and guarded. Caretakers raise the young in a communal fashion - there are no githyanki families.
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Check out p. 151 of the 2e Monstrous Manual, and behold the Gith race. It's not explicitly stated, but they seem to originally have been a Dark Sun monster. They're right before the Githyanki in the book, and both are scrawny humanoids, so I could see how they get mixed up. But when you read the description of the Gith carefully they have very little in common with the Githyanki/Githzerai.
I wonder if it was the Mordenkainen author who though the Githyanki should lay eggs, or if it's an earlier piece of lore. But I'm almost certain it's something that's been made up long after the race was introduced.
Dark Sun's gith are the descendants of githyanki who established a base on Athas before being attacked by githzerai and scattered, surviving only as the degenerated gith. See adventure module DSE2 Black Spine.