I edited your post to remove your first name and list number. The exam list and number are public documents so anyone can link your posts here back to you. It is not something you want a prosecutor doing when you are on the job.
A far as what to do to prepare physically: run.....jumping jacks...push-ups...sit-ups...pull-ups...leg lifts (lay on back legs 6" off floor & hold) and planking.
Paperwork wise: if you want to have "wroking copies" you can use to answer now, and the transfer over fresh when the time comes.....do every form here:
NYPD - Application Process
You will also need a CERTIFIED copy of your high school and all college transcripts.....each in a SEALED envelope from the institution. So DON'T OPEN THEM!.
And if you ever saw a social worker, psychologist, psychiatrist or had been to a hospital for surgery or overnight treatment.....request a complete copy of all the records from the doc or hospital. If you saw a social worker, psychologist, psychiatrist, call them and tell them what you are applying for and ask if they will write a letter to give to you, which states if what they treated you for has been resolved and if such would affect your ability to be a PO.
-In God we trust. All others, put your hands on the car and don't move.