Can I hide URL in address bar?
No you can't. Imagine spoofing https://yourbank.com/ instead of http://fakesite.com/ . The only way to see a different URL is to proxy the response, or putting it in a frame. The only way to "hide" your URL would be to use frames.
How can I hide the full URL of my website?
Type "</a>" after the link word or phrase to close off the link. Your code should now look like this: <a href = "urlofwebsite"> LINK NAME </a>, but will appear on your website as "LINK NAME" with the URL hidden.