Is 'us' a possessive noun

No, the Word 'us' is a personal pronoun, a Word that takes the place of a noun for specific people or things.

The personal pronouns are: I, you, we, he, she, it, me, us, him, her, they, them.

The pronoun 'us' is the first person, plural, objective form. The pronoun 'us' takes the place of a plural noun or two or more nouns for the speaker and one or more other people as the object of a verb or a preposition.

example: Mom has lunch ready for us. (object of the preposition 'for')

A possessive noun is a noun indicating ownership or possession by adding an apostrophe -s ('s) to the end of the Word, or just an apostrophe (') to the end of plural nouns that already end with -s.

examples:

Jack's bicycle is new. (the bicycle belonging to Jack)

From my window I can look into the bird's nest. (the nest of the bird)

The Browns' children are twins. (the children of the Browns)