Mal vs Mau:
"Mau" describes the character of a bad person or thing, while Mal mostly describes doing something badly or feeling bad.
For example: "O meu chefe é mau." (my boss is a bad person), "O meu chefe canta mal." (my boss sings badly)
Examples
Ele se sentiu mal depois de comer pela primeira vez naquele restaurante.
He felt bad after eating at that restaurant for the first time.