kliphuis on "Posts list doesn't update in Desktop version of site"

Hi
I add posts to our church site http://www.southcroft.org/ which was set up by someone who has moved on. Just before Christmas, I deleted some posts but they still appear on desktop PC version of site, and later posts relegated to subsidiary\archive page.
Strangely, they site appears correctly when viewed on mobile device.
The site has the WP SuperCache Plugin and someone suggested it may be a caching error. When I look at 'Settings' for Supercache, I see the following message:—
Error: Your cache directory (/var/www/vhosts/southcroft.org/httpdocs/wordpress/wp-content/cache/) or /var/www/vhosts/southcroft.org/httpdocs/wordpress/wp-content need to be writable for this plugin to work. Double-check it.
Cannot continue... fix previous problems and retry.
WP newbie… any suggsetions