A gui on a server? What on earth for?
But yer you don't want the GUI.
I HAVE to install a gui on my server as it sometimes gets used by the wife and/or son and so needs to be able to do stuff on via gui. However, it's only a dually atom box under the tv so it's fine...however, if you were doing it "properly" a gui isn't needed...
Less stuff running means less resource usage and less stuff to crash.
Occasionally possible. But when was the last time you installed security updates *without* rebooting.
My debian server has 169 days uptime at present.
If you're gonna use it as a 'real' server, then you don't need the GUI. It only eats resources which you could use for other purposes. Install SSHd, configure sshd.conf to disallow root logins (login as a regular user and then use sudo to become root), and if needed you could configure a firewall (like IPTABLES) to only allow SSH access from a batch of IP addresses, if security is a concern (or use certificates).