problem with widgets

Hi, I recently updated to 2.2 and want to use the widget feature. But I still got a few problems, which I cant work out.

My search box in the sidebar is not recognized correctly by the widget-thingy.

The code in the sidebar.php is:

<li id="search">
<h2><label for="s"><?php _e('Search:'); ?></label></h2>
<ul>
<li>
<form id="searchform" method="get" action="<?php echo $_SERVER['PHP_SELF']; ?>">
<div style="text-align:center">
<input type="text" name="s" id="s" size="15" />
<input type="submit" name="submit" value="<?php _e('Search'); ?>" />
</div>
</form>
</li>
</ul>
</li>

But is displayed as

<li id="search" class="widget widget_search">
<form id="searchform" method="get" action="http://www.moeboll.de">
<div>
<input name="s" id="s" size="15" type="text"><br>
<input value="Suchen" type="submit">
</div>
</form>
</li>

Why does the widget tool ignore the first li and the following to lines of code, and their close-tags at the end respectevly? Why is the form code changed as well?