  In this work, we study time-like and null geodesics in a charged black hole
background immersed in perfect fluid dark matter (PFDM). Using the condition
for circular geodesics, we evaluate the energy ($E$) and angular momentum ($L$)
in terms of the radius ($r_c$) of the circular orbits. The existence and
finite-ness of $E$ and $L$ constrain the possible range of PFDM parameter
($\chi$) and the radius of the circular orbit ($r_c$). We then use the Lyapunov
exponent ($\lambda$) to study the stability of the geodesics. Then we analyze
the critical exponent ($\gamma$) useful for determining the possibility of
detection of gravitational wave signals. After that, we study the perturbation
due to a massless scalar field in such a background and calculate the
quasinrmal mode (QNM) frequencies and their dependence on PFDM parameter $\chi$
and black hole charge $Q$. Also, we compare the obtained QNM frequencies both
in the exact case and in the eikonal limit. We also calculate the quality
factor of the oscillating system and study its dependence on $\chi$ and $Q$.
Finally, we evaluate the black hole shadow radius $R_s$ and graphically observe
the effect of $\chi$ and $Q$ on it.
