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Your half-sister's curiosity is normal. It may be worse because, as you say, she has been so isolated from normal things. So here is "real life", right in her own home. It's great that your father and stepmother have given you a place to live with your new baby, and now they have to address some issues with their daughter. (Babies, single moms, 2nd marriages, nursing, body parts, etc.)
I understand that it's annoying and that you don't want to step in and do the parenting for a child whose parents maybe haven't done as much as some others might. I think you have the right to some privacy, but you could also see this as an opportunity for her. Looking at a baby's private parts is actually a good way to learn about her own body - so let her see not only what things look like, but how important it is to stay hygienic (simple things like wiping baby poop away from the urinary and vaginal openings, not toward them, for example). She can also learn the obvious, that caring for a baby is full time, and not always easy. Young girls who see that babies aren't dolls may be more likely to avoid getting pregnant at 14 if they see how hard it is for you, an adult. She sees that you are struggling without a partner (both financial pressures and time pressures) so maybe she won't idealize the "husband-baby-picket fence" fantasy that so many young girls have.
Nursing - there is a role for privacy, of course, so she shouldn't be lifting the blanket without asking you. But on the other hand, she is learning what the purpose of breasts is, which is to nourish another human. That is so opposite the message that she's getting from TV and friends and boys on the school bus. There's actually this whole movement to make breastfeeding appear normal and not sexual at all - with women being banned from some restaurants and asked to nurse in bathrooms while sitting on toilets, there's a big push-back with other restaurants saying, "Come on in, feed your baby while you feed the rest of your family or yourself, and let us give you a free beverage to keep you hydrated." So breast feeding is feeding, not baring breasts, you know? So you can have a positive influence on her.
Her question about tasting the milk can be handled simply - again, she's just curious. Tell her babies get their nutrition from breast milk or formula and it's designed to be complete nutrition and not something older kids would find delicious, and say that older kids and adults with more developed palates and tastes get nutrition from other sources. Tell her adults don't drink breast milk and even if they did, you need to save it for the baby who has no other way of getting what she needs. Simple, non-judgmental, to the point. Her curiosity may not have anything to do with her own approaching puberty - I don't know how close she is, but her interest is normal particularly for someone who isn't getting much input from her own parents.
If her mother and your father are still sheltering her, this is kind of a wake-up call for them. It's better to address things sooner and in small amounts over the years than it is to wait until a kid is 12 and already has all her "facts" from the school bus! You can encourage your stepmother to get a few books from the library (any good children's librarian can suggest some resources that are age-appropriate) and start gently broaching the subject with her daughter. Once she and her daughter find some helpful books, she can purchase something her daughter can keep in her room and refer to periodically. That leaves you off the hook and puts the mother in the driver's seat.
You can also say to your half-sister that conversations about bodies are best held between parent and child, that you know she's curious, and she's normal. A questioning child is much preferred to a kid who goes out and asks her friends or one who doesn't ask at all and then is woefully unprepared when some boy makes his move on her. So getting her mother to establish an open and welcoming environment is an important first step. Anything you can do to encourage her to work with her mother is a good step for them getting through the teen years!