My understanding is all airlines flying to/ from the EU fall under EU261. As for non EU flights there could be no compensation but this is something that will make BA, VS etc very happy. Most if not all EU airlines would also love to dump EU261 if they could.
As for inter EU flights, yes, unless Easy etc establish EU bases they will have problems. But they employ so many people and provide such huge revenues to airports, suppliers etc that again to stop them from flying would be for the EU to cut off their nose to spite their face.
TM is threatening a hard Brexit and the EU are threatening a doomsday scenario towards the UK, but these are just opening tactics before the negotiations. The EU have far much more to lose and aviation is quite small in the overall scheme of things, so I’m sure a deal will be made.
Just a small matter, free from the burden of EU regulation and taxes fares from the UK to the US, ME etc will drop, perhaps by as much as 25%. In order to get those savings EU passengers will travel ex LHR in droves much to the chagrin of AF etc.
No, a deal will be done.