Daily from April 1 to October 31: 9:00-19:00 (last admission at 18:00). From November 1 to March 31: 9:00-18:00 (last admission at 17:00).
Yes. From May 1 to September 30, Fridays and Saturdays the palace remains open until 23:00 (last entry 22:00).
About 30 minutes before official closing time.