  In this paper, we discuss the effects of nonlinear electrodynamics (NED) on
non-rotating black holes, parametrized by the field coupling parameter $\beta$
and magnetic charge parameter $P$ in detail. Particularly, we survey physical
properties of the magnetically charged black hole, thermodynamic properties,
observational appearance, quasinormal modes and absorption cross sections. We
then show that the black hole gets colder with increasing charge. Investigating
the heat capacity, we see that the black hole is thermally stable, which is
amplified by introduction of a generalized uncertainty principle (GUP) with a
quantum gravity parameter $\lambda$. Then we compute the deflection angle at
the weak field limit, by the Gauss-Bonnet theorem and the geodesic equation,
showing that the magnetic charge has a contribution at the first order. By
ray-tracing we simulate the observational appearance of a NED black hole with
thin disk and spherical accretion. We find that the parameter $P$ has a very
strong effect on the shadow radius. We consider quasinormal modes under
massless scalar perturbations of the black hole and the greybody factor. We
find that the charge introduces a slight difference in the fundamental
frequency and that the greybody factor of the NED black hole is strongly
steepened by the introduction of increasing charge. To present observational
constrains, we show that the magnetic charge of the M87* black hole is between
$0\leq P\leq0.024$ in units of M, in agreement with the idea that real
astrophysical black holes are mostly neutral. We also find that LIGO/VIRGO and
LISA could detect NED black hole perturbations from BHs with masses between
$5M_\odot$ and $8.0\cdot 10^8\,M_\odot$. We finally show that for black holes
with masses detected with LIGO so far, charged NED black holes would deviate
from Schwarzschild by $5\sim 10$ Hz in their fundamental frequencies.
