Just update the DNS on your .co.uk domain to point to your IP, or if setting up cloudflare point it to their nameservers, then point your cloudflare account to your IP. then chance the domain in your config.
And get a TCP proxy from somewhere like http://cloudexity.com/ for your client
Yes, they'll be directed to this page:
then going on the Don't have a PayPal account bit will let you pay straight through your card, it might ask if you want to make an account after but you can say no.
I'll quickly get the default habbo theme for you and edit this post with it
EDIT: dl link http://pic.findbro.me/eDgV
put the index.php into your wwwroot/htdocs folder depending on what you're using and then put the skin into skins folder