Hi,
You say that you don't want the red part of the registration form because "login is required". What do you mean by that ? If a logged in user goes on the checkout, he won't see the registration form at all. He will only see it if he is not logged in.
If you go in the config under the tab display of the configuration and set the option "registration" to "no registration" the fields Name/Username/Password/Verify Password will be removed automatically (in our commercial versions). That can't be done in CSS as there is a lot of code and security checks (to avoid hacks, spam, etc) involved so that users can't cheat and have to fill the form correctly. The email field is needed so that hikashop can send the order notification emails to the user. The "address information" text can be removed by editing your translation file in the config under the tab languages and changing that text to an empty string.