” Query 1: can it be said that a post-existential state may also exist?
Assuming the question is not intended to produce meaningless debate about word definitions or within the wiggle room allowed by the general vagueness, then possibly/probably you're inquiring about whether the term “post-existential state” could be practically meaningful, whether there are people who can't do anything of influence to anybody, except dying.
Yes, there are comatose people, they do exist, so, the answer is yes.
Regarding (still in your number 1)
” That is, once an elderly or terminally-ill person accepts their impending demise, do they not, through acceptance, return to a non-exitential [sic] state mirroring that of the child?
Earlier you defined “pre-existential state, defined as life prior to understanding that death is inevitable, as in young children”.
The only similarity to that of someone who has learned of impending death and then gone comatose, is the similarity in how your chosen description sounds to the ear.
So the answer to the comparison with children is no, that's not a legitimate comparison, that's just silly wordplay based on how words sound. If you meant something else then you would have to at least hint about it. E.g., if you meant heads empty of thoughts, then I could answer that as a scientific fact, children's heads are full of thoughts, even before birth, so then the answer is still no, but perhaps a more meaningful no.
Disregarding the "hey, similar sounds" comparison to children, if you mean that “necessarily” people become comatose (most do not), then no, but if you mean “can” then yes. These conclusions follow from just inspecting reality. Mostly people do not become comatose when they learn about some short timeframe for their demise, but some then shortly become comatose. Let me just note that it should not be necessary to ask about such things, since this information should already have been assimilated – from TV, radio, internet, newspapers etc., not to mention general education – by anyone capable of asking a question here.
” Query 2: if we define the authentic life as borne of decisions, would not the elderly and terminally-ill have only one decision left to make, viz., how to face death authentically?
Again it can be answered simply by inspecting reality, and the answer is no.