In my experience, the only time you'll need a monitor or keyboard on a WHS is if you decide to re-install for some reason.
I don't worry about what WHS says about remote access. I configured my ISA Server's firewall to forward the needed ports (TCP ports 80 and 443) and it worked perfectly, even though WHS reported it was failing.
WHS' remote access functions are taken from SBS 2003's remote access, which is pretty widely used with very few issues. There's always the possibility that it's failing because of a lack of memory.
The automated client PC backups are set up automatically when you install the WHS client connection setup on each client PC. You can see the backup history for all the clients in the WHS Management Console.