Hi Eric,
That is the correct location for the log files, as documented in these places:
I realize it's a bit odd for logs to be stored in the %AppData%\RabbitMQ directory of the administrative user who installed the service, but that is how it works out-of-the-box for the time being. It is possible to re-direct via setting system environment variables prior to installing the service.
Anyway, back to your original issue. The console output you provided is not sufficient to diagnose this issue. Most browsers have tools that will show both the full HTTP request and response, including headers, response codes, and the body. Capturing that output to a file would be very useful.
An alternative would be to use the HTTP API to create a new user. This API is documented in the management UI via a link at the bottom of the page as well as here:
If you could use curl or Invoke-WebRequest to try and create the user with verbose output enabled, that could be useful.
I just tested adding a user via the Management UI with success, using Windows 8.1 (pro), Erlang 21 and RabbitMQ 3.7.7.
Thanks,
Luke