  GRB 180720B, observed by {\it Fermi}-GBM, with redshift $z=0.653$, isotropic
energy $E_{\rm iso}=5.92\times 10^{53}$ erg, and X-ray afterglow observed by
the XRT onboard the Neil Gehrels Swift satellite, is here classified as a
Binary-driven Hypernova I (BdHN I). BdHN I are long GRBs with a binary
progenitor composed of a carbon-oxygen core (CO$_{\rm core}$) and a neutron
star (NS) companion with orbital period $\sim 5$ min. The gravitational
collapse of the CO$_{\rm core}$ generates a supernova (SN) and a new NS
($\nu$NS) at its center. The SN hypercritical accretion onto the companion NS
triggers its gravitational collapse forming a black hole (BH). An
electrodynamical process near the BH horizon leads to the long-lasting GeV
emission with power-law luminosity $L_{\rm GeV}\propto t^{-1.19\pm0.04}$,
powered by the BH rotational energy. Correspondingly, we determine the BH mass
and spin. The $\nu$NS via its pulsar-like emission and fallback accretion
injects energy into the magnetized SN ejecta generating synchrotron radiation.
This explains the \textit{long-lasting} X-ray afterglow with power-law
luminosity $L_X \propto t^{-1.48\pm 0.32}$, energized by the $\nu$NS rotational
energy. We apply this to GRB 180720B determining the $\nu$NS magnetic field and
spin. We also analyze the GRB 180720B emission observed by the High-Energy
Stereoscopic System (H.E.S.S.), at $100$-$440$ GeV energies, $10.1$-$12.1$ h
after the Fermi-GBM trigger. We propose that this \textit{short-term} radiation
of energy $2.4\times 10^{50}$ erg and duration $\sim 10^3$ s, is powered by a
"glitch" event that suddenly injects relativistic electrons into the $\nu$NS
magnetosphere during its slowing down phase.
