seagull967;
1. I have been informed that there is a display of checklists after a system failure, is this correct?
Yes, it is call the "ECAM" - Electronically Centralized Aircraft Monitor". It serves the same purpose as the EICAS on the B767 & B777.
2. If so, in the case of AF 447, did the system display a checklist or a procedure in any manner following the UAS situation?
No. The actual "checklist" is a series of memorized steps to be actioned immediately in response to a loss of airspeed indication. The actual process is, the pilot-flying calls for the drill while continuing to fly the aircraft. The pilot-not-flying actions the memorized items and then the checklist items.
If there is immediate risk to the aircraft, (ie., near to the ground right after takeoff), the memorized drill requires that the autopilot/flight director & autothrust be disconnected, a pitch attitude of 15° be established with TO/GA thrust set, and when at circuit height or minimum safe altitude, to troubleshoot the problem. If at/above higher altitudes, a 5° pitch is set and thrust is placed in the "CLB" detent. In either case, once the memorized items are accomplished by the pilot-not-flying, the paper checklist from the QRH - Quick Reference Handbook - is read and actioned and the aircraft secured for continued flight.
3. If not, is there any circumstance when it would? Finally, if it does display such a checklist or procedure, does it advise to turn the FD's off, as most UAS checklists do as a first step?
Not applicable as you'd see, but the ECAM does display the system losses and checklist items which are actioned and cleared, again using the same process as described above. Turning off the FDs is the first memorized item in the UAS drill.
4. If not, are there circumstances it would display that?
No - turning off the FDs is done in response to drills and/or checklists. Also, if one is not going to follow the FDs, (and there may be legitimate reasons for this), then they must both be turned off.