It's called "web scraping", you can Google that.
Your webhost may or may not allow "fopen" to open a URL.
Depending on version of PHP or "php.ini" settings.
You may end up searching for "PHP CURL" functions instead.
I guess it would be similar to creating an RSS Feed Reader.
That leads me to this part ... "web scraping" is not really an
ethical way to get information. You essentially are consuming
bandwidth from the other site. With permission from the other
site owner (they may be OK with it), I guess you can do it though.
That's the whole point of sites providing RSS. They can cache
the XML files and let users gather timely information. The host
of the RSS feed stays in control of the information and the
caching (which affects the bandwidth).
I'm not going to provide any snippets because in my opinion, it's not ethical.