Donnie was supposed to die from the engine. When he didn't, it created a rift between two dimensions. The whole movie takes place in essentially an alternate dimension, where Frank is dead, because Donnie shot him ... in the originating dimesion. Frank's ghost appears to Donnie in the alternate dimension to lead Donnie through all the steps he would need to take, to finally understand that he has to die, or the rift will destroy the universe.
In the special features of the original dvd (haven't checked on the director's cut yet), you can read through some pages of the time travel book. It definitely explains a lot. The director's cut, some of the scenes are shown with an overlay of some of the book, that kind of explain what's going on during the following scenes.
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