This tutorial describes how to change the logo: https://www.zen-cart.com/tutorials/i...hp?article=125
Neither the cart nor search code will work in Zen Cart, as they refer to files from your old cart.
You can copy the existing search box to a spot right after
PHP Code:
<!--bof-branding display-->
<div id="logoWrapper">
<div id="logo"><?php echo '<a href="' . HTTP_SERVER . DIR_WS_CATALOG . '">' . zen_image($template->get_template_dir(HEADER_LOGO_IMAGE, DIR_WS_TEMPLATE, $current_page_base,'images'). '/' . HEADER_LOGO_IMAGE, HEADER_ALT_TEXT) . '</a>'; ?></div>
PHP Code:
<div id="navMainSearch"><?php require(DIR_WS_MODULES . 'sideboxes/search_header.php'); ?></div>
and put your own content around it.
PHP Code:
<div id="customSearchHeader">Product Search:
<div id="navMainSearch"><?php require(DIR_WS_MODULES . 'sideboxes/search_header.php'); ?></div>
</div>
The cart/header is available in Free Addons, and you can put the code for that just above the customSearchHeader div.
Then you can style both of those in the stylesheet, with float: right; and some other properties as required (like headivider.gif as a background at the top of the search div). If you do the PHP code changes, I can advise on tweaking the styling.