  [Abridged] By appealing to a Quark-Nova (QN; the explosive transition of a
neutron star to a quark star) in the wake of a core-collapse Supernova
explosion of a massive star, we develop a unified model for long duration
Gamma-ray Bursts (LGRBs) and Fast Radio Bursts (FRBs). The time delay (years to
decades) between the SN and the QN and, the fragmented nature (i.e. millions of
chunks) of the relativistic QN ejecta are key to yielding a robust LGRB engine.
In our model, a LGRB light-curve exhibits the interaction of the fragmented QN
ejecta with a turbulent (i.e. filamentary and magnetically saturated) SN ejecta
which is shaped by its interaction with an underlying pulsar wind nebula (PWN).
The afterglow is due to the interaction of the QN chunks, exiting the SN
ejecta, with the surrounding medium. Our model can fit BAT/XRT prompt and
afterglow light-curves, simultaneously with their spectra, thus yielding the
observed properties of LGRBs (e.g. the Band function and the X-ray flares). We
find that the Yonetoku law and the Amati law are not fundamental but
phenomenological. FRBs result from coherent synchrotron emission when the QN
chunks interact with non-turbulent weakly magnetized PWN-SN ejecta, where
conditions are prone to the Weibel instability. Magnetic field amplification
induced by the Weibel instability sets the bunching length for electrons and
pairs to radiate coherently. The resulting emission frequency, luminosity,
duration and dispersion measure in our model are consistent with FRB data. We
find a natural unification of high-energy burst phenomena from FRBs to LGRBs
including X-ray Flashes and X-ray rich GRBs as well as Super-Luminous SNe. We
find a possible connection between Ultra-High Energy Cosmic Rays and FRBs and
propose that a QN following a binary neutron star merger can yield a short GRB
(SGRB) with fits to BAT/XRT light-curves.
