Quokka
With regards to Eurocontrol, you have to have a passport from one of the Eurocontrol member states which is roughly the EU plus some more countries.
There was Conversion Courses for Eurocontrol but none are being offered at the moment, and policy has changed towards training of new abinitio controllers. If you want to join Eurocontrol going through the abinitio avenue would be your only option and would be quicker than waiting for Conversion Courses to be advertised. The Abinitio intake is open and courses commence roughly every 6 months. There is an upper age for Abinitio recruitment which is 25.