Local PC cache stays filled with old WordPress Site data

Unsurprisingly so since you tell browser to cache everything for 1 month by default (ExpiresDefault "access plus 1 month").

You should limit long caching times to static resources and leave pages served by WP out of it.

My go to resource for .htaccess configuration is HTML5 Boilerplate.

It works with WP nicely and correctly excludes web pages from agressive browser caching (ExpiresByType text/html "access plus 0 seconds").