Get rid of User Name Password info in Check out fo

If your users are already logged in when they reach the checkout, they won't see the registration form.
That form is specifically for users to register when they are not logged in.
When they are logged in, they will see a new button they will be able to click on in order to display the address entry form.

The login form and the address form being separated, after both on the page without the field at the top won't work. The address information will just not be used by the system. In that case, you would have to hide the whole registration area on the right with CSS like that:
.hikashop_checkout_login_right_part{display:none;}

You can change any text in HikaShop by doing a translation override:
www.hikashop.com/en/download/languages.html#modify