Which type of subordinate clause is 'Were I a reach man' in the sentence - 'Were I a reach man, I would help the poor.'?

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