Is "it" used as a demonstrative pronoun like "that" or "this" in these situations and is the speaker pointing to the objects mentioned?
My friend sees a beautiful ring on my finger and asks me "What is it?"
My sister puts something she has just bought in the supermarket and I ask her "What is it?" She is holding it in her hand or it is near her on the table.
"It" is sometimes used like a demonstrative pronoun. But "it" isn't a demonstrative pronoun, it's a personal pronoun and it doesn't explictly point to something near or far from the speaker.
It, as a personal pronoun can refer to any object the identity of which is understood by the context. The context can be linguistic (an object previously mentioned) or the wider context of the environment
In the examples you give, "What's that?" is more likely as this does "point" to a particular object. You should ask "What's that on your finger?" instead of "What is it on your finger?"
