why was it set up that way?
really there is no reason why the whole site shouldnt run using just wordpress, it would be simple to transfer the design over to the word press and run the whole site through that. It would look and function in exactly the same way, seems you've went an extremely over complicated way when you really didnt need to.
If you are intending on selling products through a shop on your site, you will need to unmask your address, it needs to be visible on the domain registration details if you are using that domain to trade through. It can be left as registered to dark horizon studio but it cant be left as a UK individual with the address masked, its law Im afraid (although scotserve would know more about that than me, seeing as it's part of his job really)
another option would be to install a cart on the site, style it the same as the main site and run it that way, I still think stripping the site back to just the wordpress and just using that with an ecommerce plugin would be the best option.
Either way, in answer to the original question, yes you can bolt on a shop to the existing website, plenty of different ways you could do it though
