  We study many-body entanglements and spectra of the extended bosonic
Hatano-Nelson model in the hard-core limit. We show that the system undergoes a
phase transition from a gapless phase to a charge density wave phase
accompanied by a $\mathcal{PT}$ transition in the first excited state. The
phase transition is characterized by the crossing of the ground-state
biorthogonal order parameter and the sudden change of the first excited-state
entanglement entropy. The gapless phase is verified by the logarithmic scaling
of the ground-state entanglement entropy with the central charge $c=1$.
Furthermore, we show that all energy spectral clusters would form ellipses in
strong nearest-neighbor interactions, for which we establish a universal
scaling law. The lengths of the major and minor axes are shown to obey power
laws with respect to the nearest-neighbor interaction. The exact expressions
are derived for the numbers of energy levels on the outermost elliptic ring of
each clusters.
