Can a member perform the duties of the Speaker if he/she has not been appointed by the President?
No, a member cannot perform the duties of the Speaker if he/she has not been appointed by the President. The context states that while the office of Speaker is vacant, the duties of the office shall be performed by the Deputy Speaker or, if the office of Deputy Speaker is also vacant, by such member of the House of the People as the President may appoint for the purpose.