The last two links look fine, so the cache issue sounds more likely. Certainly worth ruling out.
rel=“stylesheet” is the way to go.
Whether you use www in your urls or not is up to you, but it’s best to decide to use one or the other always. Choose one, then rule out the other via .htaccess. Otherwise search engines will treat them as separate and divide ranking between them. (See half way down this page: http://www.sitepoint.com/forums/showthread.php?t=670928)
Hmm, the obvious answer would be ‘empty it’, but are you asking about what to do on an ongoing basis? Are you sure it’s a problem on an ongoing basis? I’m sure I’ve emptied the IE cache before, but I rarely use it so have to Google how to do it every time. (I’m normally on a Mac.)