This creature becomes an exact copy of a copied card, except that it also has Dimir Doppelganger's activated ability. If it becomes a copy of a different creature card, the new copy will overwrite the old copy.
A permanent's ability that refers to cards the creature exiled (such as Sisters of Stone Death's third ability) only affects cards exiled by other abilities intrinsic to that permanent (such as Sisters of Stone Death's second ability). Suppose that (a) Dimir Doppelganger copies Arc-Slogger, (b) its "deal 2 damage" ability is activated, and then (c) it copies Sisters of Stone Death. Creatures exiled by Arc-Slogger's ability can't be returned with Sisters of Stone Death's ability.