I think, If you are using cPanel you should add the new domain and subdomain first. then point your domain to the IP via A record or CNAME.
CNAME is duplicating the target's hostname/domain IP record. CMIIW
agreed, I'm using firefox on ubuntu, every HTML pages (even URL rewritten) that do not contain caching HTTP headers is cached (such as this forum page)
maybe the browser is forced to interpret any .css files as stylesheet while .php not. If you go to .php site and .html site then you press back button, you should know that the source code of html pages are cached while .php pages are not. So, the browser is programmed to handle some extensions...