Is the word sing a common noun?

No, "sing" is a verb. It describes an action (the act of producing musical sounds with the voice).

A common noun is a general name for a person, place, or thing. Examples of common nouns include:

* Person: student, teacher, doctor

* Place: city, park, school

* Thing: book, chair, computer

Since "sing" describes an action, it's not a common noun.