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As an educated guess, what happens if you add google's nameserver at 8.8.8.8 to /etc/resolv.conf and retry?

Assuming I'm right, ot should sort the issue with gdm denying root login. As far as the wifi goes, have you checked the module is loading at boot? systemd is rather more stroppy about blacklists than...

Check /etc/pam.d/gdm-password, look at the third line and the issue should be obvious. ;)