1. Not sure what the transportation situation is when you cross into the North. I suppose it depends on which crossing you use - the Metehan/Ayios Dimitrios crossing is the most used one in Nicosia and the only one in Nicosia where cars can cross, the Ledra St and Ledra Palace crossings are for pedestrians only). Perhaps you can arrange in advance to have a taxi pick you up at the crossing and take you to the airport? It's about a 35-40 min ride from the Metehan crossing to ECN. If you have your transportation arranged in advance, if you crossed at midnight, you'll have more than enough time for a 03:30 flight. If you decide to do this, I can try and find some contact info for a taxi for you. I'm not sure if taxis hang out at that crossing at that time of night. BTW ECN has just opened a new airport, about 5 miles from the old one. It's having some "new build" issues to work out.

2. If you fly into LCA and leave via ECN, there will be no record of you ever leaving the RoC (the RoC does not recognize ECN as an legitimate airport). This is only an issue if you ever plan to come back to the RoC. This applies to both UK and Canadian passports.

3. You should not have any problems in AMS.