mouseout dalay 500 ms

Try this:

<!-- top menu -->
<script type="text/javascript">
function mainmenu(){
jQuery(" #nav ul ").css({display: "none"}); // Opera Fix
jQuery(" #nav li ").hover(function(){
jQuery(this).find('ul').css({visibility: "visible",display: "none"});
jQuery(this).find('ul:first').css({visibility: "visible",display: "none"}).<?php echo $menuAnimationEffect; ?>;
},function(){jQuery(this).find('ul:first').fadeOut(500,function(){ jQuery(this).css({visibility: "hidden"}); }) });}
jQuery(document).ready(function(){ mainmenu();});
</script>

P.S. You don't have to persuade us with "around" words to help you. For small things like this we are always willing to help.

Thank you.

But this was again not the right code.
The menu does not react as it shoud.
It becomes even worse! Not functioning correct in other things as before.

Therefore I have written more things to persuede you.
Because I am using this template for more than a year now.
Now I am getting more and more visitors and they are frustrated because of the missing functionallity of the menu.

Someone misses animation effect? Maybe I don't understand what you want then. You want drop-down menu not to disappear immediately after mouse losses focus over it instead you want delay of 500ms before panel disappears?

As I understand you correct - yes. The same at it is with the menu at the left site. If the mouse goes away it takes some time till the submenu closes.

Well maybe best you pay for some custom job time so we could better design it. Send contact email using "Report To Moderator" if you are interested

Well, that's very strange. I have payed for the template that have this bug.
You yourself have written: "For small things like this we are always willing to help."

I am not sure that you are able to solve this problem.

After so many times you have not even understood what the problem is, have always written wrong codes.

Iff someone really know about the things he is doing, than it's really a "small thing". Than its just a small addition to the code and the work is done. It takes him less than 5 minutes.
And for this short time I am willing to pay.