Learn Russian: Ей не хотелось говорить об этом.

Just like the приходится (have to) construction from this lesson, хотеться (to feel like) is an impersonal verb. It does not take a standard subject. Instead, the person experiencing the feeling is put in the Dative case (ей), so the sentence literally means "to her, it was not desirable."

What is the difference between saying "Она не хотела" and "Ей не хотелось"?

Она не хотела is a direct, active statement meaning "She did not want." Ей не хотелось is softer and describes an internal mood or state, meaning "She did not feel like it." Using the impersonal reflexive verb хотеться makes the lack of desire feel like something that just happened to her rather than a firm, active decision.

Why does "хотелось" have the neuter past tense ending "-ось" if we are talking about a woman?

In impersonal constructions, there is no grammatical subject in the Nominative case for the verb to agree with. When a past tense verb has no Nominative subject to match, it automatically defaults to the neuter singular ending. For reflexive verbs, this neuter ending is -ось.

Why use the imperfective verb "говорить" here instead of the perfective "сказать"?

Говорить means "to talk" or "to discuss" in a general, ongoing sense, which perfectly fits the meaning of not wanting to have a conversation about a topic. The perfective сказать focuses on the single, completed result of saying a specific phrase, which does not fit the idea of "talking about it."