Permission to leave Dubai
Chill. It's a non-issue, and not really related to EK, let alone the pilots. It's based on local 'labour laws', as a preventative agianst the labourers absconding.
Same applies to the cars that take us to work - we are just the labour being delivered to work - also required under the laws.
As for applying for being absent from Dubai - just log on to the pilot site and submit it. The 'accept' response is automatic.