The rewrite rule is not working on the site and I don't see the joomulus instance to see what it's doing.
The basics ...
suhosin and other server protections are designed to prevent cross-server attacks so they consider a link within joomlabear.com/page1 pointing to www.joomlabear/page2 to be a link coming from outside with the effect that it's also by an unregistered user initiating a new session.
The crossdomain file will instruct the server to treat the other domain as a friendly insider.
You should be using the htaccess that came with joomla, called htaccess.txt and rename it to be .htaccess The rename may make it disappear if you do not have permission to view hidden files. It has a line that turns mod rewrite on. The code above should go there as the first rewrite executed. All it does is if www is in the URL, it removes it so if you typed in the address bar
www.joomlabear.com with this code working, it would instantly be replaced with joomlabear.com
This allows you to write all your links with or without the www and they will still work, more importantly, a link from an external site to
www.harabara.com/apage will still allow joomulus to work because it will immediately be changed to harabara.com/apage.
All three joomla SEF buttons in global config. should be 'On'.
Ahem - this whole thread is assuming no third party SEF is active. Likewise for a third party search enhancement that needs a different URL. Do you have sh404SEF or similar running?
The third issue is how you have your links constructed in the joomulus parameters page. local links should start from your root directory.
tag: tagged page
URL: /search/tagged&20page.html
Size: 20
the url may also have a search type appended such as 'all words' or 'exact'.