Hi Networkz,
Welcome to Flyertalk (and the CX section).

Most of your questions are answered in the FAQ. Check
section 10 for the difference between MPC and AM. Everything you could ever want to know about it is in there.
And if you read the
CX official FAQ item 8, it says you can claim miles for up to 6 months after you fly. So sign up for AM first, then submit requests for mileage credit for all your flights in the last 6 months that qualify.
Note that with CX not all fare buckets are eligible to earn miles. If you simply bought the lowest possible economy fare each time, chances are that some of your flights might not even have miles for credit.
As long as you are a member of AM, CX will usually give you a free MPC membership as soon as you qualify (30k flight miles inside a year for most cases).
-RJ