Hi Kayle,
There are a lot of components, modules and plugins that use either the cache folder or their installation folder to deliver scripts or stylesheets. Recently Joomla updated the robots.txt file to disable bots from accessing those folders and hence the whole mess. All the static files should originate from the folder media, this is the recommendation from Joomla, but it seems that developers are abusing that!
Root folder most probably will be the folder public_html in your server. It is the folder that also has configuration.php and index.php.
To verify the permissions just head on administrator to System->System Information and then select the tab Directory Permissions. Everything should be green there.
Regards