My 66th birthday is the last week of September, 2016. If I want to draw 100% of my FRA retirement amount (I believe that is called my PIA), would my first month of SS retirement benefit be earned in September, paid in October, or would it be earned in October, paid in November?

Robert,
Your first month of SS retirement benefit will be earned in September and you will receive your first check in October.
Best,
Mike