The Problem is very simple:
#Domain: localhost
The domain points to localhost but should point to your domain.
it should most likely be:
#Domain: www.yourdomain.com
Every part of the .htaccess file that points to localhost needs to be updated to www.yourdomain.com. Looking at your images section, every entry there needs an update.
RewriteCond %{HTTP_HOST} ^localhost$
needs to be
RewriteCond %{HTTP_HOST} ^www.yourdomain.com$
Another Issue is:
RewriteRule . - [E=REWRITEBASE:/presta/]
That actually only works if your prestashop installation is in the folder /presta. If not it should look like this RewriteRule . - [E=REWRITEBASE:/]