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1. In terms of building regulations you may wish to read the document here, this outlines the current regulations. However in summary you can place the consumer unit (fuse box) on the outside wall providing there are not pipes running above or behind the planned location. The consumer unit will also need to be mounted between 0.45and 1.2M from the floor, which is probably a lot lower than it is currently, and you need to consider how to keep it away from children and pets. The second thing you need to consider is the cost of moving the company fuse, this can only be arranged by the electricity board, and they may have their own requirements over and above building control.
2. Low water pressure is a common issue, you need to first identify if you have a gravity or mains fed system. If there is a water tank this is a gravity system and normally the cause of low water pressure, however its very unlikely you would have a gravity fed system if you have an apartment. If you have a gravity fed system (and want to use it) you need to take the water source from as close to the hot and cold water tanks as possible, if your going for an electric shower you need to take the water source from as close to the in house stop cock as possible. If you have a combi boiler (hot water on demand), you need to take the hot water feed from as close to the boiler as possible. I would suggest you use 22mm pipe, to reduce further water pressure issues regardless of which option you select.
3. You can use water pumps to increase the pressure such as the ones found here. The challenge is they can be very noisy, and if you do not place them in the right place every time you turn on a tap the pump starts, rather than only working when you turn on a shower.
4. Installing a wet room requires high level of skill to ensure the room is water tight. Firstly you need to ensure you are using the right product for the job, both in terms of membrane and adhesive, secondly you need to inspect the membrane to ensure there are no folders, creases or holes where water may penetrate. Lastly I would use a damp meter while the shower is running and go around the outside of the proposed wet room and check there are no signs of leaks.
I hope this helps clarify your questions, this are all very important questions, and it may be worth asking for quotes from trades and asking their input, since seeing what actual room your converting and how your plumbing is currently setup may give you additional options or obstacles you need to overcome.