The time that you get off the ship depends on what group you are in, and what you will be doing. On my 2006 cruise on the Liberty, disbark announcements started at 6:30 AM for the people on Carnival tours to Holy Rome, etc. Then other groups are called based on needs. I think by around 9 or 9:30 all guests would have been off. I was called a little after 8 for the transfer to a Carnival hotel in Rome.
Be sure to tell the purser the night before if you need to get off the boat early due to an early flight. Otherwise, maybe let them know you do not have anything pressing and can debark at a later time. Since my flight does not leave until after noon for my up coming cruise, I am hoping that I will be one of the last to disbark. I would rather sit on the ship (in public areas so room steward can get the cabins ready for the next guests) in comfort then milling about FCO for hours.
Yes, you still get breakfast that morning. I did not do the sit down breakfast so do not know if that is open. However, the Lido buffet breakfast is definitely open and with the usual full slate of offerings.