  After revisiting the heterotic string-derived low-energy effective model of
\cite{Ashfaque:2016ydg, Athanasopoulos:2014bba, Faraggi:2016xnm,
Ashfaque:2016jha} constructed in the four-dimensional free fermionic
formulation, we find two axions which are either harmful or massive. As a
direct consequence, they can not solve the strong $CP$ problem which is in
complete agreement with \cite{Lopez:1990iq, Halyo:1993xn}. We also explore the
possibility of the self-interacting dark matter residing in the non-Abelian
gauge group present in the hidden sector \cite{Faraggi:2000pv}. We find that
the low-energy string-derived model naturally welcomes the self-interacting
dark matter as $4$ copies of the non-Abelian, hidden $SU(2)$ gauge group factor
are present.
