1. Yes you have to state ALL the grades you got. 2. Just Merit or Distiction, but some people put their percentages - so bascially it's up to you. 3. Yes, an AEA in maths just tests your ability on A-Level Maths, but in a more advanced way.
You do if your school is certificating your grades. You don't if they are not. I got this information from my exams officer AND from UCAS customer help line
With regards to the certification thing, a U in the AEA will NOT get certified under any circumstances, regardless of your school's "policy".
2) I put "Dist" because "Distinction" doesn't fit and UCAS told me that's fine. "Merit" would fix in the box so put that. Your maths AEA results slip will not give you a mark anyway (you'd have to ask your teachers).