The log entries are being saved to the global log file I imagine. I'm not sure how to setup separate log files for a location. I know you can do it with virtual hosts.
What you wrote in the initial post should work. Are you sure root user is allowed access without password? maybe you already logged in as the root user? after logging in once with the basic authentication, your status is stored in a session. Try it in another browser where you are sure you are not logged in already and see if it asks for the password
I have not been testing it through a browser but through ssh (i.e. > svn co htpp://....)
And for some reason if you are logged in as root on the other box, then it does not ask for a password, even though the user root has a password (something random, that even I dont know).
You should test is through the browser then. I am not sure about this, but I think that if you run an http request to a SVN service on the same server, it's smart enough to rewrite it as a local link (file:///..).