how long does it take to receive a duplicate title by mail?

A bank will not reissue for an original title after loan payoff. So very important to register title with your home of record state! Can't request a title from a state dmv that has never recieved one! If all your ducks are in a row; no back taxes or registration etc you should be able to request one in about a week.

3 weeks

Not sure. Maybe 3 mo