For your need

1/ With [extension by grum] Advanced Menu Manager parameter Quick schearch / About / contact

2/ Go to admin install and Activate plugin LocalFiles Editor

3/ Go to Administration -> Plugins -> LocalFiles Editor -> tab 'templates'

Create new file

File name -> personalmenu
submit

add code

{foreach from=$block->data item=link}
<dt>
        {if is_array($link)}
            <li><a href="{$link.URL}" title="{$link.TITLE}" {if isset($link.REL)}{$link.REL}{/if}>{$link.NAME}</a></li>
        {/if}
</dt>
    {/foreach}
   
<dt>
{if isset($block->data.qsearch) and  $block->data.qsearch==true}
    <form action="{$ROOT_URL}qsearch.php" method="get" id="quicksearch" onsubmit="return this.q.value!='' && this.q.value!=qsearch_prompt;">
      <p style="margin:0;padding:0"{*this <p> is for html validation only - does not affect positioning*}>
        <input type="text" name="q" id="qsearchInput" onfocus="if (value==qsearch_prompt) value='';" onblur="if (value=='') value=qsearch_prompt;" style="width:90%">
      </p>
    </form>
    <script type="text/javascript">var qsearch_prompt="{'Quick search'|@translate|@escape:'javascript'}"; document.getElementById('qsearchInput').value=qsearch_prompt;</script>
  {/if}
</dt>

save file

4/ go to Administration -> Configuration -> Templates

for line personalmenu select for collum 'Original templates' menubar_menu.tpl
submit

5/ look at your site
Is that what you want ?

[If you made a personal theme, you can also add in the template directory, a file menubar_menu.tpl with this code]

Hello ddtddt,

many thanks for the stuff you made for me during last days. I really appreciate it!
Almost everything is working as we expected, there are only 2 cosmetic things to be corrected.
First, when you click on "About", menu bar disappears. And the second is that "search" form overflows menu bar.
Do you think you could dedicate to this a bit more of your time please?

Thank you,

Marekh ( www.marekh.sk)

yes, this is exactly what I searched for.
thanks!