If we use the term "predestination", we may assume then that a particular outcome will occur regardless of the actions of the certain agencies. In theological parlance, predestination should be distinguished from double predestination, the latter of which refers to all people being predestined either for salvation (the elect) or damnation (the reprobate). Predestination encompasses only those who are eternally saved, not those who may be eternally damned. Most mainline Christians will espouse predestination; Calvinism trends toward double predestination, though you will find many in the Reformed tradition (e.g., Karl Barth) who do not hold for double predestination.
This theological aside is helpful for understanding the use of predestination as it applies to Equestria. Broadly speaking, there does seem to be some sort of irrevocable destiny for every pony -- hence the existence of cutie marks and latent skills associated with those talents found even in "blank flanks." I hesitate to apply "predestination" because of the theological overtones; but if it is meant to imply that all ponies eventually discover a particular talent, then I would agree that such is the case. "Destiny" is probably the better term, as it is used quite frequently in the show. Throughout the show's history, nopony has ever denied or refused their destiny when confronted with it. The Cutie Mark Crusaders may not embrace their natural talents, but that appears to hinge more on tunnel vision and their obliviousness as opposed to refusing to follow their skills.
But could Twilight, for example, have refused Celestia's offer to fulfill her destiny? I'm not so sure she could. The most by way of diverging from the cosmic plan, so to speak, are events such as Luna's transformation into Night Mare Moon -- but even then there was an eventual reconciliation. Based on what we know so far, destinies cannot be delayed indefinitely; sooner or later, you'll need to follow a path determined by your skills. "Magical Mystery Cure" demonstrated how even ponies with improper cutie marks were beholden to their destinies, even if they were improperly implied. One wonders if there are ever ponies who effectively end up with incorrect cutie marks; however, Twilight's spell in "Magical Mystery Cure" and its aftermath were treated as complete breaks from the norm. Whatever talent and/or destiny is bestowed upon a pony, they are naturally inclined to pursue and enjoy the associated activities.
It's largely treated as a legend by most ponies. There's no explanation apart from ambiguous assertion that the stars would aid in her escape. Celestia recognized the impending danger in some fashion, prompting her to send Twilight to Ponyville to make friends. She even mentions that she knew Twilight possessed the magic to defeat Night Mare Moon. How she precisely knew this is a mystery.