BLEED FAULT lamp illumination under various conditions
The question is quite broad but here's my understanding..


  However, when there is an emergency condition e.g. engines are lost/off/unavailable (i.e. no generators) and also no APU possible, should there be any bleed fault?


No, since there is no fault (as you've listed). The bleeds are in the correct config and there is no disagreement between the valve and the switch. There is just no pressure to the system. You will get a 'Bleed Off' indication if your switch is on with no pressure to the valve(type dependant). Also you will get a pack off indication - if you've got the bleeds set to feed the packs.


  I know that you have things like built-in autotest stuff that goes on before the computers are powered, but surely when the aircraft is on batteries/emergency power, should there be any bleed faults?


As I said above you wont get faults, but you may get indications that the bleeds are off.