From what I remember from Latin courses years ago (please correct me if I make a mistake):
Illa is more like "that woman", 'woman' being implied by illa being feminine singular. But can be translated simply as "she".
Haec (added this for contrast) is more "this woman" but can also be used like "she".
Ea is more a general 'she', can be used for 'this' or 'that' woman.
Yes, they are demonstratives. More details: http://dcc.dickinson.edu/grammar/latin/demonstrative-pronouns-paradigms
Illa is far the more unnatural here I feel. Is, Ea, Id is the literal He, She, It. Using Ille, Illa, Illud is more for emphasis. THAT woman, her, she is the one we're talking about: as opposed to She is doing it. I don't think we should base new word instruction on one of the 3rd of 4th uses of a pronoun. I know Ille, Illa, Illud can sometimes be He she or it as a Latin teacher, but I don't tell my students that at first. Got to build from the basics.
Then why do I not get to use both in the answers? Also, I checked the OLD, made a post with both definitions to be sure. Is, Ea, Id, is used as He, she, it first. Ille -a -ud is used as That first. I'm not seeing That introduced as it's first meaning in the course. So I'm getting the wrong impression. If I didn't know the language I'd run around thinking Is, Ea, Id, and Ille -a -ud are interchangeable, and while they are in SOME situations, they definitely are Not in others.
Coming from a language that, just like Latin, uses demonstratives far more specifically than English does, I can definitely say that "ea" and "illa" are NOT intechangeable.
Ea expresses gender and third person. That's all. Illa creates a strong sense of distance and disconnection (just as haec creates a sense of physical proximity!). I would argue that the meanings of distance, gender, and person are equally relevant for such demonstratives and I would strongly suggest NOT to use demonstratives (be it pronoun or adjective) in contexts where remarking distance is not required.
Ea est benigna = She (the person I am talking about, whose gender is feminine) is kind. Illa est benigna = She (the person I am talking about, whose gender is feminine, and who's far away) is kind.
In short, yes. This could refer to anything that is grammatically feminine, not just biologically female humans, though "benigna" does mean "kind-natured", so it is not often used to describe things other than people or things imbued with a person's kindliness, such as their words, minds, acts. Exceptions to this tend to come from the poets.