Here's my Pointless Theory! While there is a lot of guess-work in it, I feel it is overall consistent with the Manga translated to date. It is in three parts: Solaria Speculations; A Fanciful Sequence of Critical Events; and Miscellaneous Odds and Ends.
PART I: SOLARIA SPECULATIONS -
Long ago, during humanity's Hunting and Gathering period, a sufficiently large number of tribes of humans came together having, purely by random, some slightly anomalous behavioral and physiological traits. These proto-Solarians formed a society whose social conventions increased the selection pressure for these traits.
The first trait started as a tendency to poke lions and such with sticks - just to see what would happen. This tendency evolved into the classic "Must... Push... Button!" and "Pull the Rope!" behaviors. Small children also display this trait when they try stuffing a slice of toast into a VCR slot.
The second trait initially was to get really excited about poking the stick mentioned in Trait #1. This became a trigger for the body to release the large amount of energy needed to, in many cases, run away really, really fast. This trait sometimes manifests itself as "Genki-ness", though not exclusively so.
The third trait started as a slightly-better-than-normal ability to heal wounds, including the regeneration of fingertips and earlobes (this is known to occur today in rare instances and is a topic of current research). This healing ability was particularly valuable if the proto-Solarian wasn't a quite fast enough runner. Using the energy released using Trait #2, this healing ability eventually developed to what can only be described as "Really Awesome!"
The forth trait is the retention of some chimpanzee-type muscle fibers (they can rip you apart, I've heard). This is probably a minor evolutionary throw-back (NOT what you might be thinking). The ability to punch out a lion probably impressed possible future spouses, and so was inevitably selected for.
The fifth trait is a bit of a mystery, but appears to be some kind of 'quantum neural resonance' (I haven't a clue, so I'm making this up) that allowed one proto-Solarian to sense where other tribe members were while on a hunt-and-gather outing. This ability was also useful in keeping track of your spouse - and led to many fights. As the Solarians developed advanced technology, this ability stimulated research into areas like quantum computing, personality and memory recording, and neural-pattern-sensing locks that would only respond to specific individuals.
One thing of particular relevance is that present day humans may have weak versions of these traits, but are unable normally to activate them. In a sense, we don't know which mental button to push - but a Solarian 'ghost' does! 'Pushing the buttons' in a non-Solarian body may not result in as strong an effect as in a real Solarian, but if you really lean on it...
PART II: A FANCIFUL SEQUENCE OF CRITICAL EVENTS -
20,000 years ago
--- Solaria is Destroyed.
--- Kabapu seals the memories, personality, and neural patterns of Her Majesty (Her Excellency?) into the Core, and then freezes the body.
--- The Solarian survivors disperse, taking what they could save of their technology with them.
During the 200 Centuries following Solaria's Destruction
--- Solarian survivors gradually die (or are killed).
--- Kabapu searches out 'Overtechnology', acquiring or destroying it.
--- Kabapu goes into some kind of stasis for long periods (thus the problem of answering what his 'age' is).
Recent Events Timeline starts (time "T" in years after Kabapu/Tenmangu meeting at T=0)
--- T= 0: Tenmangu starts work on the future Ropponmatsu, and analysis of related 'overtechnology'.
--- T=+?: Miwa Rengaya joins Tenmangu in his work, studying the biotechnology-related aspects of 'overtechnology'.
--- T=+3: Based on Miwa's studies, 3 cloning experiments are initiated using frozen/preserved Solarian tissue. (These experiments took place in the facility Kabapu ordered demolished in Vol. 9.) Since the cloning process used proceeds at the same pace as normal human development, each experiment was spaced 9 months apart. The first clone was a pure clone using the preserved Solarian tissue. The second clone used some of Miwa's DNA as a 'superior substrate'. The third clone used (forgive me, Elgala!) some of Kabapu's DNA. This explains the hair. The three female clones were initially designated "A-Ko", "B-Ko" and "C-Ko", for some unknown reason.
--- T=+4: While the cloning was going on, Miwa and Tenmangu decided to do their own 'cloning' experiment, and so Gojyou was born.
--- T=+8: By now, the three little girls had imprinted on Miwa as their Mama, and Tenmangu as their Papa (whom they adored), with occasional visits from "Uncle PuPu". The child care-taking staff were elderly women who were 'mean' to the little girls (according to the girls). The Evil Old Woman! A-Ko decided Papa's joking reference to "Your Excellency" meant her name should be "Excel"; B-Ko misunderstood "You're so quite" as "You're Hyatt"; and C-Ko (who liked to play dress up and admire herself in mirrors) heard "You're so Elegant" as "You're Elgala".
--- T=+9: The second part of the cloning experiment was attempted, which was to imprint a copy (a 'ghost'?) of Her Majesty on the girls' minds. After several attempts - which failed utterly - Miwa and Tenmangu realized the girls' young brains were changing too rapidly for the imprinting to work. They would have had to wait another 15 years before the process could be expected to succeed.
--- T=10: The girls were separated and sent off to various 'academies' for care and education. The trauma of being taken from their 'parents' caused them to forget their early childhood and each other. In desperation (and perhaps to find out things that Kabapu might be hiding from them) Tenmangu attempted the imprinting process on himself, using the 'ghost' of some fellow named 'Il Palazzo'. The result was a disaster! The two personalities couldn't integrate properly, so a confused Tenmangu/Il Palazzo went into hiding. Miwa, in turn desperate to help her husband, refined the process and tried imprinting herself with Her Majesty's personality. While integrating the two personalities, Miwa claimed illness and avoided Kabapu, returning 'changed'.
--- T=??: After graduating from the Academy she had been placed in (which specialized in Science and hand-to-hand combat), Excel goes through many part time jobs. Eventually Excel is subconsciously drawn to find Il Palazzo/Tenmangu.
--- T=??: Hyatt finds ACROSS.
--- T=??: Elgala finds ACROSS.
--- T=30: Gojyou Shiouji appears in the Manga.
PART III: MISCELLANEOUS ODDS AND ENDS -
1) Excel is approximately the same age as Gojyou Shiouji, perhaps a half year older.
2) Hyatt is 9 months younger than Excel, and Elgala a year and a half younger than Excel.
3) Kabapu doesn't recognize that Il Palazzo is also Tenmangu, because he's 20,000 years old! The memory is bound to be a bit bad at times.
4) Actually, Tenmangu has simply changed enough in appearance, style, personality and age, that Kabapu sees who he expects to see: Il Palazzo!
5) Excel, Hyatt, and Elgala are all in love with Il Palazzo because subconsciously 1) they recognize him as their 'Papa' from childhood, and 2) Her Majesty's adoration for Il Palazzo is manifesting itself.
6) Tenmangu/Il Palazzo is conflicted about Excel, because he knows he's married to Miwa, and Il Palazzo/Tenmangu knows that Excel is not truly his Solarian love.
7) Although Miwa and Tenmangu/Il Palazzo are not physically Solarian, their implanted knowledge of which 'mental buttons' to push allows them to access some Solarian capabilities.
8] Hyatt's genes apparently got hooked up backwards, so that excitement causes pre-emptive death, with all her energy stored for resurrection when she calms down.
9) Elgala has her resonant neural projection ability stuck in the 'ON' position with the volume set at 'HIGH'. Everyone just assumes that she's talking out loud.
10) I'M REALLY TIRED NOW. I'M GOING TO GO TAKE A NAP.
WHEW! I'm sure I've left out a bunch of things, but I hope you get the idea.