As far as EBT (early buddhist texts) go, I'm pretty sure there's nothing to support any of your ideas on what happens to the body of any arahant after nirvana.
There is this SN 47.9 Gilāna sutta, where the
buddha is close to death but prolongs life, and limits body pain with animitta samadhi, but not all arahants could do that. Otherwise his arahant body after nirvana (while alive) seems to be just as frail as any normal human:
I’m now old, elderly and senior. I’m advanced in years and have
reached the final stage of life. Āsītiko me vayo vattati. I’m
currently eighty years old. Seyyathāpi, ānanda, jajjarasakaṭaṃ
veḷamissakena yāpeti; Just as a decrepit cart keeps going by relying
on straps, evameva kho, ānanda, veḷamissakena maññe tathāgatassa kāyo
yāpeti. in the same way, the Realized One’s body keeps going by
relying on straps, or so you’d think.
And there are the suttas where the Buddha and Moggallana say had they chosen to, they could have extended their lifespan for the remainder of the aeon. But this has to do more with supernormal powers, which arahants may or may not have developed, it doesn't have to do with what happens to everyones' body after nirvana realization. The EBT's AFAIK don't explain how that ability of remaining for an aeon works. Theravada commentary (which I disagree with) says that 'aeon' is to be taken figuratively as being able to live out a natural human lifespan (100 years or so). I suspect what that power to live out for a remainder of an aeon really means, is living out the aeon in a ghost state in a mind made body (for reference, a lower brahma realm has a lifespan of one aeon). There are accounts of taoist masters doing something similar, not yet taking rebirth in their next form, but hanging around in some kind of intermediate state with ability to communicate with their disciples in the human realm.
Regarding the ability to sleep less, nor not sleeping at all and remaining conscious all the time, the EBT's do mention some things regarding that, but nothing specific only for an arahant.