  We give a modified definition of a reproducing kernel Hilbert $C^*$-module
(shortly, $RKHC^*M$) without using the condition of self-duality and discuss
some related aspects; in particular, an interpolation theorem is presented. We
investigate the exterior tensor product of $RKHC^*M$s and find their
reproducing kernel. In addition, we deal with left multipliers of $RKHC^*M$s.
Under some mild conditions, it is shown that one can make a new $RKHC^*M$ via a
left multiplier. Moreover, we introduce the Berezin transform of an operator in
the context of $RKHC^*M$s and construct a unital subalgebra of the unital
$C^*$-algebra consisting of adjointable maps on an $RKHC^*M$ and show that it
is closed with respect to a certain topology. Finally, the Papadakis theorem is
extended to the setting of $RKHC^*M$, and in order for the multiplication of
two specific functions to be in the Papadakis $RKHC^*M$, some conditions are
explored.
