I found these notes on gzhandler;http://phptutorial.info/?ob-gzhandler
ob_gzhandler() requires the zlib extension.
You cannot use both ob_gzhandler() and zlib.output_compression. Also note that using zlib.output_compression is preferred over ob_gzhandler().
I don't know if that is an issue with your server though.
You seem to be having a session issue, have you checked to make sure your directories are writable? In the Joomla backend go to Help/System Info and click on the Directory Permissions tab, make sure all your folders are writable.
Try running the Forum Post Assistant
on your site to see if it find any issues.
Have you tried a different browser to see if the slow site problem is browser based?
If your site has a lot of data you could be having a database problem, the database server may be slow or your database may need repair. Using phpMyAdmin try doing a repair on your database, do a backup of the database first.
Try replacing the two files that have errors with know good copies from the same version of Joomla you are using;
I just checked and this is not a core file;
I think I have seen a j added to file names during file updates, could it be an update that went bad, or could it be an extension that has replaced the core factory.php file with its own? It may be that you have an extension installed that is saving its own session cookie and it is having the problem.