(1) Yes, they have to be an EASA instructor.
(2) If the licence and class rating are still in date - yes you can. If they aren't, no you can't.
(3) You'll need to fly training as required, then a proficiency check with an EASA examiner. I don't *believe* that you have to come to the UK for that.
(4) Only CAA can formally answer this question, but normally if it's lapsed, it's lapsed. Flight with an instructor only for now. I can't see them being sympathetic - it was up to you to fly with an EASA instructor in that year, and to check that their qualifications were correct. I don't think that you'll find them very helpful.
G