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I feel I must have heard this but am now not sure. Can I say

Los ancianos vivimos en regiones litorales

assuming I am old myself of course. Possible options which occur to me

Nosotros ancianos vivimos en regiones litorales

Nosotros, los ancianos, vivimos en regiones litorales

but neither of those sounds quite right to me.

This is OK:

Los ancianos vivimos en regiones litorales. ✅

and this too:

Nosotros, los ancianos, vivimos en regiones litorales. ✅

This one is not (it looks like a direct calque from English):

Nosotros ancianos vivimos en regiones litorales. ❌

The first two sentences are perfectly idiomatic. I believe that the second one should be written with those parenthetical commas but is in fact often not.

The grammatical analysis of these constructions is subject to some debate. There's some material about it in the Nueva Gramática de la Lengua Española (NGLE), beginning at §33.6j. Some grammarians analyze these subjects as the sum of an implicit first person plural pronoun plus a "covert specifying apposition", i.e. the first two sentences that I've marked as OK would be equivalent, the former having a hidden nosotros, the latter making it explicit.

Yes, of course. The sentence

Los ancianos vivimos en regiones litorales

is perfectly valid in Spanish and denotes that you are an old man yourself. In fact, your second other option is also quite right, but maybe a specific context is needed (it could work as part of a longer dialogue in a novel or such). The first one ("nosotros anciamos vivimos") is incorrect.

Here's what the Spanish Gramática says about that:

33.6j Cuando la función de sujeto es desempeñada por grupos nominales en plural que designan personas (los habitantes, las madres, los docentes), la concordancia con el verbo puede establecerse en tercera persona del plural (Los habitantes de las grandes ciudades viven en un continuo ajetreo), pero también en primera y segunda persona del plural (Los habitantes de las grandes ciudades {vivimos ~ vivís} en un continuo ajetreo). [...]

33.6k La primera persona del plural implica [...] la INCLUSIÓN del hablante en el grupo designado por el sujeto. La segunda implica, paralelamente, la inclusión del oyente en ese mismo grupo. Ambas implicaciones desaparecen si la persona empleada es la tercera. [...]

In English:

When the function of the subject is performed by nominal groups in plural form that designate persons (los habitantes, las madres, los docentes), the agreement with the verb can be established in the third person of the plural (Los habitantes de las grandes ciudades viven en un continuo ajetreo), but also in the first and second person of the plural (Los habitantes de las grandes ciudades {vivimos ~ vivís} en un continuo ajetreo). The first person of the plural implies the INCLUSION of the speaker in the group designated by the subject. The second implies, in parallel, the inclusion of the listener in that same group. Both implications disappear if the employed person is the third.

So you could also say

Los ancianos viven en regiones litorales

and then you would be saying that you do not consider yourself part of the group of old men, or maybe you are an old man but you are stating that from an outside point of view, as in

La humanidad vive tiempos difíciles