As their father went out, they started feeling more insecure. What type of Adverb Clause is the underlined one?

He became rich overnight. What part of speech is 'overnight'?

The nightingale is a singing bird. In this singing is a/an --

I Came home after the rain -----.

The Doctor took the round in the hospital. Here 'round' is a/an ---

Alumni is the plural from of