Previous posts have covered your questions to a large extent but with some confusing data.
There are a number of differences between 747 Classic aircraft and the 747-400.
Hydraulics
All 747’s have 4 independent systems. Each system is powered by an Engine Driven Pump (EDP) as the primary power source and a “Demand Pump” as a supplemental source.
On a classic 747’s all demand pumps were Air Driven Pumps (ADP’s). On a standard 747-400 only systems #1 & #4 had the same ADP’s and #2 & #3 had ACMP’s (AC Motor Pumps) since they did not need the high flow rate of an ADP. However, some operators requested Boeing to install ADP’s in all 4 systems. On a standard 747 there is a low output AC pump in #4 system for ground towing. Some operators requested an identical pump in #1 system.
In flight the “Demand Pump” in system #2 & #3 never operated unless there was a failure of the EDP or the engine was shut down .
The ADP in systems #1 & #4 always operated during gear and TE Flap operation as the EDP could not meet the flow demand on its own.
There are no APU driven hydraulic pumps. Use a Demand Pump (whether ADP or ACMP) for hydraulic power using bleed air or electric power from the APU.
A 747 APU cannot be used in flight for electric power.
Electrical
There are 2 batteries, Main & APU. They are charged whenever the aircraft is powered regardless of source.
There is a Standby Power system which powers the very essential loads which is probably confusing as this is more important than the Essential Power system ie. the Standby Power system powers less equipment than the Essential Bus system. Yes, it is all avionics and last ditch avionics at that. There is an inverter that powers very essential avionics loads only. If all engines fail a 747’s windmilling engines’ provide enough hydraulic power to maintain control without recourse to a RAT or use of electric pumps provided speed is maintained above a certain figure.
Pneumatics
Wing Anti-Ice air exits to ambient via slots in the lower surface.
Contrary to some previous posts Wing Anti-Ice is inhibited on the ground. It is only available in flight regardless of LE device operation. The only inhibit is air/ground logic.
Catalytic converters fit between the Pack Valve and primary heat exchanger but are an optional feature. There is 1 heat exchanger per pack. The heat exchanger physically is a single unit but has two separate flow paths: primary and secondary The air flows from the Pack Valve to the primary section then to the ACM and back to the secondary section.
The heat exchanger in the nacelle is a Precooler, which reduces the bleed air temperature to the temperature required by the pneumatic and air conditioning systems. It may be installed in the pylon or on the engine depending in engine type.