He killed his own brother lest he should disclose his crimes. What type of part of speech is ‘lest’?

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