To merge the two boxes, create an over-ride information.php in includes/modules/sidesboxes/YOUR_TEMPLATE_NAME.
Then pick up lines 17-25 of includes/modules/sidesboxes/more_information.php and drop them into your new version of information.php where you want them to appear. As you do so edit the $more_information[] array to be simply $information[].
These links should now show up in the information box and you should turn the more_information box off via Admin > Tools > Layout Boxes Controller.
To change the names of the links go to your inlcudes/languages/YOUR_TEMPLATE_NAME/english.php file where you will find the following two blocks of code that define the text used for the links in these boxes> // information box text in sideboxes/information.php
define('BOX_HEADING_INFORMATION', 'Information');
define('BOX_INFORMATION_PRIVACY', 'Privacy Notice');
define('BOX_INFORMATION_CONDITIONS', 'Conditions of Use');
define('BOX_INFORMATION_SHIPPING', 'Shipping & Returns');
define('BOX_INFORMATION_CONTACT', 'Contact Us');
define('BOX_BBINDEX', 'Forum');
define('BOX_INFORMATION_UNSUBSCRIBE', 'Newsletter Unsubscribe');
define('BOX_INFORMATION_SITE_MAP', 'Site Map');
// information box text in sideboxes/more_information.php - were TUTORIAL_
define('BOX_HEADING_MORE_INFORMATION', 'More Information');
define('BOX_INFORMATION_PAGE_2', 'Page 2');
define('BOX_INFORMATION_PAGE_3', 'Page 3');
define('BOX_INFORMATION_PAGE_4', 'Page 4');
How you change pages 2, 3 and 4 depends what you want to do with them and there are multiple answers depending upon this objective, including via the define pages editor in Admin, direct editing of the languages/english/html_includes files and creating new php files if you wish them to be more dynamic.
