The easiest way to handle this is to let your domain point to the WordPress directory, in your case: /mysite from your root web folder. This usually can be done either by your hoster or in your cPanel/administration tools.
You also have to change WordPress Url and Site Url in your WordPress Settings to your new Domain.
If you have no way of changing the directory your domain points to on your server, you can COPY (not move) the index.php from your WordPress folder to your root directory, as well as the .htaccess.
Inside the index.php in your root directory you have to change the include path of wp-blog-header from
require('./wp-blog-header.php');
to
require('./MySite/wp-blog-header.php');
And change the WordPress Url in your WordPress Settings to http://www.mysite.de/MySite, so WordPress knows that it’s files are located in a Subdirectory.