Nobody can access the urls that you posted, because they are under /admin. This path is protected and only to be seen when you are set up as a site-wide administrator.
For question 3 you could check the serverlog inside /log of your aolserver home directory. What is even better is to get watchdog running. You can see watchdogs output via your browser. The path is /admin/monitoring/watchdog. If nothing is displayed, you have to copy the aolserver-errors.pl to /servers/yourserver/bin of your aolserver home directory. You find this perl script in /web/yourserver/bin/.
I never seen the problem with categories that you are having.
