To answer your 2 questions from your original post:
1) Go to any major domain registration site, such as namecheap.com and buy the domain. Set the DNS servers to ns1.x10hosting.com and ns2.x10hosting.com. Go to your account panel and on the left side you will see an area where you can change your information. One of these will be an option to change your domain.
2) That depends - if you have your links set to index.html and folder/index.html then your links are fine. However, if you have your links set to name.x10hosting.com/index.html, you will need to change them. (That is why for the future I always recommend the first way.)