Are you sure it is the default cPanel FP extension installation?
I wonder what FP extension feature were you using? the global admin site which can be used to enable/disable FP extension for each vhost? admin page for each site which can be used to manage user accounts? or uploading through FP extension from a windows machine.
The global admin site will not work under cPanel and it is not needed at all, cPanel will enable FP extension for each site automatically, no need to go through the global admin site. The other two features work well.
Default cPanel FP extension for each vhost does not use /usr/local/apache/conf/httpd.conf, instead, each vhost has a dedicated fake configuration file under /usr/local/apache/conf/sites/... , httpd.conf is not touched by FP extension for normal use.
And it may not be possible to make the global admin site work under cPanel, as /usr/local/apache/conf/httpd.conf is only readable to "root" user, and it is not desireable to run the FP extension CGI as root, problem 3,4,5 are related to it directly, problem 8 probably is caused by that as well.