To remove links from the Information box, follow these steps.
1. Go to the File Manager in your store admin (found at the bottom of Tools>Define Languages).
2. Edit the file found in includes/boxes/information.php
3. Remove the link you need.
To remove View Cart, take out this line:
'<a class="infoBoxContents" href="' . tep_href_link(FILENAME_SHOPPING_CART) . '">' . HEADER_TITLE_CART_CONTENTS . '</a><br>' .
To remove My Account, take out this line:
'<a class="infoBoxContents" href="' . tep_href_link(FILENAME_ACCOUNT) . '">' . HEADER_TITLE_MY_ACCOUNT . '</a><br>' .
The rest of the links are handled by your store's Page Editor section.