The nouns in the sentence are bird, branch tree, song.
Two nouns: 'nurse' and 'patients'. Although in some other uses 'visits' can be a noun, in that sentence it is a verb.
There are two nouns in your sentence: inventors and talents.
Bird is the noun. Black is an adjective. The is an Article Adjective. And I think is is an Article Adjective too but I don't know.
No, singing birds in the sky is a clause that is missing a verb. Singing birds in the sky do what? Because it is a clause, it cannot be a complete sentence.