Can "Esta" mean "he" or "she"?
 

I have the following, and am interested in the use of "Esta" in the bolded parts. It seems to be used like the words "ella/él". Is that right? :



—¿Estas mejor, Nina? —preguntó María, la madre de Marcelina, que había entrado en el camarote en ese momento. Esta le respondió con un murmullo.

—Debería tomar el aire, señora —dijo Ana—. Le vendrá bien para adecuarse. Además, hay un día fabuloso.

—Tienes razón, Ana. Nina, cariño, ¿serás capaz de levantarte? Tu padre está en la cubierta con unos compatriotas que comparten destino con nosotros.

Esta torció el cuello hacia dónde se encontraba su madre.

In both of the sentences you made bold, the pronoun esta means 'the latter' and a female is the referent-the girl who murmured and craned her neck. To reference a male, the pronoun este is used. To refer back to the last topic/idea, use esto.

Hmm.. I'm still a bit confused about how "the latter" makes sense here. Do you know of any resource that maybe talks about this usage? I can't seem to find anything about it.

There can be some confusion, especially when you consider that esta and este, when followed by a noun, are adjectives (technically, demonstrative adjectives), and when no noun follows, they are demonstrative pronouns.
Add esto to this group. You can also include esa, ese, eso, aquella, aquél, and aquello.
These pronombres demostrativos can be translated as 'this (one), that (one), and this/that idea. Plural forms also exist.

The gender-specific ones can be used to refer to a thing or a person that has already been introduced. They are often translated into English as 'the latter' or 'the former', depending on which pronoun was used.

The referent initially named remains unchanged, unless context calls for a change.
In your original post, the referent in the story didn't change. We know this because 'esta' was used both times, even though a male was introduced in between.

There isn't a lot said about using the demonstrative pronouns as a way to indicate 'the latter' or 'the former', but this is very common usage. It is mentioned in dictionaries and the DPD. In a good dictionary, look at the pronoun usage. One of the meanings for esta/este is 'the latter' or 'the last (one)' (of things mentioned). Other dictionaries say 'of two' instead of 'of things mentioned'. 'The former' or 'the first (one)' is said aquella/aquél.

Here is a sentence I readily find online. Look at post #3 in the thread for the sentence labeled = the latter. Jorge is 'the latter', while Luis is 'the former' (the poster there used 'the other one', but 'former' could be substituted and mean the same thing). (The thread deals with whether an accent mark is needed on este (shown in the thread title with an accent and without one) or no. You can include esta. Esto (also in the thread title) never takes an accent mark. The rules changed decades ago, but you'll see that the DPD does include one example when, to be clear, an accented form would be required in formal writing.)

Some usage examples:

- Me suscribí a un periódico en italiano. Este me sirve para practicar lo que aprendo del idioma. -> "Este" = "un periódico"
I bought a subscription for a newspaper in Italian. It's useful for practicing what I learn of the language.

- Estoy con el doctor José Pérez. Este dirige el Instituto de Lenguas Extranjeras de la Universidad Nacional. -> "Este" = "el doctor J.P."
I'm with Doctor José Pérez. He is the director of the Institute of Foreign Languages in the National University.

- Los pingüinos son aves acuáticas. Estos viven en el Polo Sur. -> "Estos" = "los pingüinos"
Penguins are aquatic birds. They live in the South Pole.

- Nunca disgustes a tus padres, pues estos siempre buscan tu bien. -> "estos" = "tus padres"
Never antagonize with your parents, because they always look after your well being.

- Compré un libro de Julieta Fierro. Esta es la Científica más conocida de méxico. -> "Esta" = Julieta Fierro
I bought a book by Julieta Fierro. She's the best known scientist in Mexico.

- Las personas que me rodean son las más importantes, pues de estas aprendo todo el tiempo. ->"Estas" = "las personas"
The people who surround me are the most important, because I learn from them all the time.