1.A non EU operator to operate within Europe even under for example the guise of being Easyjet (Hungary), financially it needs to be 51% EU money.
2. From the day after Brexit, UK (non-EU) Pilots will not have any automatic right to live and work in Europe. Pilots will be hoping that each individual country sets up a new bureaucratic system to issue them work permits and put them onto local taxation.
I understand that Britain will also have to provide work permits for Europeans based in the UK but as it is Britain leaving the EU it would follow that Britain will be ready to do that. Other nations will not.
Don't be under any illusion: a British Pilots with a non-EU passport will be worth a lot less throughout his career. A Brexit will cost UK Pilots very, very Dearly.