If you REALLY don't care there is no need whatsoever to tell her anything about it. You probably DON'T care about what the huge majority of rest of the world says or does - but you don't feel a need to go telling all of them that you don't care.
Truth is you probably DO care what your sister says and does, and I believe it would be better to tell her the truth. If what she says upsets you tell her so and ask her not to do it, tell her you don't set out to upset her and you wish you could get on better.
If what she does annoys you tell her what it is that is annoying you. Tell her you don't like being annoyed with her, that you don't set out to deliberately annoy her, and that you wish you could both be in the same place without annoying each other.
Girls are usually much better than boys at spotting when something is a lie, and knowing when someone is upset or annoyed. If you try to pretend that you don't care she will know that is getting to you and will feel that it is perfectly fine to continue to annoy and upset you when she wants to because you told her yourself that you don't care about it.
Be honest about your feelings, or just completely ignore the things that you don't like as though you didn't even notice them.
Trouble is, if you make her believe that you don't care about her, it will start to make you more and more distant, in later years you are more likely to lose touch with one another, and she might not be there for you when you need her.
-- Best wishes - Majikhise.
About what..? Just tell her that whatever it is doesn't really interest you. Have some interesting topics handy and whenever she starts talking about whatever it is that you don't care about then change the subject, if possible.