It's great to have immediate feed back from no less than three pax on this flight (and welcome to Lucky27 and Pawky). Firstly, it is wonderful that everyone is safe. The crew did a good job.
As far as compensation is concerned, just research the statutory allowance. You may be sure that EZ are just as upset as you are. I suspect that their confused reaction is that they have never had a double failure like this. The reason for the DIVERT was passenger illness. The reason for the precautions on LANDING was due to a technical failure.
Had the flight not diverted, then the failure would probably have been discovered on approach to LGW. The two incidents are not related and the relief crew might very well not have been told about the tech problem. Their job was to get out to Athens and collect pax from a flight diverted due to medical emergency - which is true.
As to the aircraft being despatched from Larnaca not ready, the answer is No. Because that means the end of the airline. European airline technicians don't play roulette with the company. Not least, any crash and deaths are then on their signature ...
With regards to 'boot the computer 45 minutes' and then the concern that you leave more quickly: I have experienced this before (not with EZY) and I think the cabin staff should have said: "They may have to reboot the computer, which can take a bit of time." If it can take 45 minutes? Best not to say. It sounds like they were trying to be helpful and were not to know that - for whatever reason - the aircraft would be ready to move more quickly.
Lastly, it is wonderful that everyone is safe. The crew did a good job.
For the record I do not work for any carrier and never have.