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The title of ths topic was hard to find...
Several problems, several questions but 1 Goal:

I have 20 pages and some updates are hard to follow as my site grows ( ie : menu).
So, I extracted my menu and put it into another file and saved it apart as topnav.html in folder "includes"
To call now my menu into all my .html files I inserted the following :

<div id="header">
<?php include('includes/topnav.html'); ?>
</div>

To be able to parse the php include I input the following in my htaccess file which look like that now ( note : my site runs with Apache CGI / Php5

RewriteEngine on 
RewriteCond %{THE_REQUEST} ^[A-Z]{3,9}\ /index\.html\ HTTP/ 
RewriteRule ^index\.html$ http://mysite.com/ [R=301,L] 
AddHandler application/x-httpd-php .htm .html #THIS IS THE CODE I FOUND EVERYWHERE ON THE WEB TO ALLOW MY PHP TO BE PARSED.
# Error Pages
ErrorDocument 404 /index.html
#Other rules blahblah...

So far no luck.
If I try to change my extension to .php it works, but I do not want to do so, as it will hurt my SEO.

What do i do wrong ?
I've previously asked to my provider and he told me to use the addHandler instead of addType directive.

On the other hand, I also found in my researches on the web, that taking out all file extension is the best right now.
so that files look like www.mysite.com/the-story instead of www.site.com/the-story.html

To sum-up:
How can I use php include in all my html files and remove all file extensions and how ?

I hope my question(s) won't be too messy ...
THANK you very much.
I have spent 2 days on this. I am stumped.