Hi, I never had anything to do with green goddesses but I was a firefighter a few years ago and still remember some stuff.
The pole on the roof is a ceiling hook used to pull down burning or suspect ceilings. The portable pump is usually called a "featherweight pump", later versions took 4 to carry comfortably !
The chimney rod would normally be with a stirrup pump and nozzle with a roller for putting out chimney fires, also bucket, canvas bag and salvage sheets.
The large hard hoses are suction hoses used to supply the vehicle pump or portable pump.
I don't know if the GG has a single or two stage pump. It would have a centrifugal pump, normally the first low pressure stage would supply the larger soft hoses with around 5 bar at the branch and then the second stage would supply the hose reels with I think around 15 bar, The hose reels are known as high pressure jets, normally.
It would be good to see the pump tested, there will be a standard test in the operation manual.
The Jack is for lifting the axels near a wheel not to lift the chassis.
Hope that is some help.
Iain