What exactly was the plan and how did Dan help him with it? In the end Dan talks to a doctor or someone and convinces him to accept Ben's heart to save Emily's life. Who exactly is Dan in the movie apart from being friends with Ben.
Dan is the living executor to Ben's will, once Ben dies.
In order for Ben to ensure that his remaining body parts (heart and cornea) are given to Emily and Erza, Ben had to establish a will and then assign someone to carry out its details upon the event of his death. This person is generally referred to as an executor.
"An executor is a legal term referring to a person named by the maker of a will or nominated by the testator to carry out the instructions of the will. ... The executor's duties also include disbursing property to the beneficiaries as designated in the will, obtaining information of potential heirs, collecting and arranging for payment of debts of the estate and approving or disapproving creditors' claims."
If Ben hadn't of gone through the process of creating a will and legally establishing that Emily and Ezra are to receive his remaining organs/tissues, then, it would be at the state's discretion as to who gets them ..
.. And, in all probability they wouldn't go to Emily and Ezra, but instead, to patients who are either in immediate critical condition, and/or on a waiting list of some kind.
An unfortunate case of this occurring IRL: a mom had kidney failure and was on dialysis for several years; the son was tested as a positive match, but before a transplant took place the son was killed; the mom then tried to get her son's organ to save her own life, but she couldn't because no legal effort was made to establish that the mom should receive the kidney upon her son's [untimely] death.
Mother in need denied her slain son's kidney