With hot water requirements you can apply a certain amount of diversity same as you can apply to electrical peak loads. Unless you have a massive family or a small guest house I wouldn't size the heater to the maximum possible hot water requirement. I have 5 bathrooms with 3 showers and 2 baths between them and we have a 150litre HWC immersion heater, we don't ever run short of water even though the same sized cylinder would be used in a single bathroomed flat for example. I think you've convinced yourself you need a 14.4kW heater but I think it would be worth getting some professional advice from a plumber before committing to the capital outlay and high installation costs of such a large system.
In answer to your last question you can get anyone who's competent to perform the installation. I personally would get a plumber to install the heater and the pipework and get an electrician to install the supply and isolator etc.