The adaptor plate requires that you run the EA82 flywheel - you will need to elongate the bolt holes to bolt it to the EJ22.
To fit the gearbox you’ll have all the usual issues of 5spd fitment. Many threads on this.
Power steering AFAIK requires the rack from another MY of the same era. Then adapt the hoses of the EJ system to the MY rack.
AC: use the MY wiring, but wire the over pressure and low pressure switches in series to make the compressor work. You will need to adapt the hoses to connect everything up. The EJ ecu will have a reference wire for AC to trigger the Thermo fans.
And that EJ22 isn’t overheating because of the water pump. It’s the head gaskets replace these while the engine is out.
Cheers
Bennie