The taxi driver is Zeus, or Hades, or a collective apparition of the Greek gods
As is pointed out within the film itself, the name of the ship, Aeolis, is a reference to the figure of Greek mythology. His father, Sisyphus, was condemned - by Zeus, by Hades, or by all the Greek gods, depending on how you interpret the old myths - to forever roll a boulder up a hill, only to see it roll down again, a fate clearly intended to mirror Jess's imprisonment in the time loop. Zeus, or Hades, or whichever god/gods inflicted this punishment upon Sisyphus, clearly felt that Jess deserved the same punishment for abusing her son; so they created the time loop, then manifested themselves in the human world in the form of the taxi driver in order to lure Jess into the loop's beginning. Poor Jess is, in other words, doomed to repeat this experience for eternity.
Heather doesn't exist
Heather is listed on the main page under What Happened to the Mouse?
because after she falls off she's never seen or mentioned again. If you go with the theory that Jess is in purgatory and this is her punishment then it's possible Heather only exists in purgatory (for whatever reason) and vanishes after she's no longer relevant.