Is Niece a Common Noun?

A daughter of someone's sibling, brother-in-law, or sister-in-law; either or one's brother ("fraternal niece") or of one's sister ("sororal niece").

Is nephew a common noun?

As detailed above, 'nephew' is a noun.

Is Uncle is a proper noun?

The word ''uncle'' is a common noun, but when it is paired with a specific uncle's name, then it transforms to a proper noun.