Hello Adam,
Do I detect that you have not had the caravan very long, and you may not have had all the instruction books?
I think you have to seperate problems. The first is the lack of water at bathroom and kitchen taps, and the second is no hot water.
From your description of how you can get water when the shower is turned on, but not when any of the other taps are turned on this makes me suspect that you have a water system that relies on microswitches in each of the taps to turn the pump on. All the microswitches are wired in paralell so the pump should run whwnever any tap is turned on. It is not uncommon for one microswitch to fail, but what is puzzeling, is that so many micro switches seem to have failed at the same time! This makes me think that some wiring between the switches may have becom disconnected or damaged.
The lack of hot water, in a 1998 caravan the origonal water heater would be a Carver Cascade 2GE. The heater does not act instantaneously, its more like a domestic hot water cyclinder sytem whci takes time to warm up. The GE referes to the fact it can be heated by Gas or mains electric power or a combination of both. I assume you know the heater holds 9Lt of water and it takes about 15Min before any warm water will be available. It reaches full temperature in about 25 to 30min. This applies to both the gas or electric heating, if gas and electric are used together you will get some warm water after about 10 mins.
These are points that should really have been detected at its last service.