Usta technically equals "mouth" (oral cavity = jama ustna), that's why you can say "She has her fingers in her mouth" - "Ona ma palce w ustach".

But it's very often used to refer to lips, for example you rather won't talk about applying lipstick on 'wargi' (although that's actually the word for lips: sg warga, pl wargi), but on 'usta'. And here it's a situation like that. It's used for lips a lot more often than the word 'wargi' itself.

Oh, also "usta" in any meaning is always plural, check here for clarity.

Good question. It just seems.. more technical. Would feel strange (at least to me) in many contexts.

Besides, "wargi" have another meaning in the female anatomy (labia), so using the word sometimes may allow for someone to make a not-very-ambitious joke...

If you assume that they are blue because of sickness or cold, then yes, 'sine' can work just fine. Added now.