Basic Active Service Date is when you came into the military and swore in. For some that is about a week prior to Basic Training, for others, who were in the Delayed Entry Program, that can be months before basic training.

PEBD is what finance uses to determine credible time you are getting paid for.

I have 12 years of Active Federal Service but I am getting paid for 16 since I got out and went National Guard for four years. But this is only for pay purposes. The four years will not count for retirement unless there was active time in there.

Yes - NMMI is both a prep (high) school and accredited junior college. While some HS graduates go straight to the service academies, many others who may have been denied initial entry will be offered the opportunity to attend after a year in one of the many Academy prep schools, of which NMMI is one.

NMMI offers the Army's Early Commissioning Program (ECP) and graduates the highest number of Army lieutenants outside of the USMA. A cadet in the ECP will have either 3 years of JROTC or have attended Basic Camp (not the same as Basic Training), and may be offered a billet with a local NG ADA unit nearby, and be paid as an E5 while doing this monthly drill. Upon graduation from NMMI with an AA degree, the cadet will be commissioned as a USAR 2LT and be given 3 more years to finish the BA or BS.

Either way, it's a win-win. Prepping will improve the chance of being accepted later into a service academy, but if that falls through the cadet will still be able to be commissioned in one more year - and your contract date is the pay entry base date (PEBD) which is factored into retirement.