As far as I know, you would have to remove the "search bar" codes part, or section...to the sidebar.php file, rather then having it in the header.php file.
In control panel => Presentation => Themes => Themes Editor =>...Click on the header.php file link. then edit from there.
This part, as far as I know:
<form action="<?php echo $_SERVER['PHP_SELF']; ?>" method="get">
<input value="<?php echo wp_specialchars($s, 1); ?>" name="s" id="s" />
<input type="submit" value="Go!" id="searchbutton" name="searchbutton" />
Relocate this coding from the header.php file, to the sidebar.php file...some where within it.
To be able to have more links at top. But it also depends on how many pages you have to start with. If you want 20 pages, or so...you'd have to add them pages (meaning the links to the pages) to the sidebar.php file.
Please tell me different, moderators, or ppls...
It all depends on your intentions..so please let us know what that is..so we can help you with it. =)
Also, please be warned, you'll need to change the background and such, via the CSS file, if you move it to the sidebar.php file. It's not hard, but, you'll have to, when moving it. =)
Also, there is more ppl out there using Blix then I, so maybe they'll be able to help you more.. =)