On our comp:
The f/o will remain PF if it was PF before the emergency.
The cpt will not assign f/o as PF if a emergency is on course and cpt is PF.
In case of eng fire:
After V1-cancel fire bell (PNF)
Above 400' ,a/c under controll,gear up -PF calls for the recall items on eng fire/sev damage & separation ,and after checking with the PNF the correct engine selected ,disengage a/t &reduce thrust then dictate the rest of the recalls and PNF executes-start levers,fire switch....
Check the QRH ,CI for recomendations regarding use of checklists.
Brgds Alex