So, aircraft engines usually provide thrust, and also power 3 types of systems: bleed-air pneumatic, hydraulic, and electric. Correct? With exceptions, like 787 which has no bleeds.
How do the power requirements of those four compare?
Bleeds are commonly shut down deliberately in lower levels to gain thrust.
Now, as for the systems listed:
* Cabin lighting and cabin entertainment system
Agreed (really no way to do it by bleed air or hydraulic)
As mentioned, usually a bleed-air system. But how do they heat or cool air as needed? In any case, 787 has no bleeds, so this would be suited to electric rather than hydraulic application.
* Galley food preparation system
Agreed. I do not think there is any actual fire in galleys.
* Hydraulic pumps or actuators
* Flight controls
Are those electrical, or hydraulic?
I think most planes where all hydraulic systems drain will lose all flight controls except throttles, like 747, DC-10 and A300. However, VC-10 has some kinds of local hydraulic pumps - how are those powered? And A380 has 2 general hydraulic systems plus local hydraulic pumps - powered by what?
* Navigational system and radio communicaton
* External lights, strobo-light, spotlight to tail fin.
* Any other electrical devices (?)
Like black boxes.
A MD-11 famously flew for several minutes after the black boxes stopped recording because their electric supply was broken by fire.
However, each engine has a generator, the auxiliary power unit in the tail has an identical generator.
Identical in capacity? So, 3 generators in total.
However, capacities like this are irrelevant for pilots. They load shed automatically if load is excessive.
Do pilots have any discretion, about which systems they plan on using and which they think unsafe to power up?
all fuel pumps off, all electrics off, all carbon life forms off, move away from machine as soon as possible! Sounds sensible with loose fuel around!
On ground, yes...
In air... you presumably would not want to shut down all engines and ditch at a heavy weight and with most of fuel still in tanks because some of the fuel is loose around the plane.
and emergency loads like alternate flap drives.
A 747 has no rat. Do windmilling engines provide as much electricity as working ones? Can the flaps be driven solely by windmilling engine electricity?
Generally, are there any electric systems on a plane which should never intentionally be shed or switched off before the plane has come to rest on ground or water?