  In the second work of this series, we explore the optimal search strategy for
serendipitous and gravitational-wave-triggered target-of-opportunity (ToO)
observations of kilonovae and optical short-duration gamma-ray burst (sGRB)
afterglows from binary neutron star (BNS) mergers, assuming that cosmological
kilonovae are AT2017gfo-like (but with viewing-angle dependence) and that the
properties of afterglows are consistent with those of cosmological sGRB
afterglows. A one-day cadence serendipitous search strategy with an exposure
time of $\sim30\,$s can always achieve an optimal search strategy of kilonovae
and afterglows for various survey projects. We show that the optimal detection
rates of the kilonovae (afterglows) are $\sim0.3/0.6/1/20\,$yr$^{-1}$
($\sim50/60/100/800\,$yr$^{-1}$) for ZTF/Mephisto/WFST/LSST, respectively A
better search strategy for SiTian than the current design is to increase the
exposure time. In principle, a fully built SiTian can detect
$\sim7({2000})\,$yr$^{-1}$ kilonovae (afterglows). Population properties of
electromagnetic (EM) signals detected via the serendipitous observations are
studied in detail. For ToO observations, we predict that one can detect
$\sim11\,{\rm{yr}}^{-1}$ BNS gravitational wave (GW) events during the fourth
observing run (O4) by considering an exact duty cycle of the third observing
run. The median GW sky localization area is expected to be
$\sim10\,{\rm{deg}}^2$ for detectable BNS GW events. In O4, we predict that
ZTF/Mephisto/WFST/LSST can detect $\sim5/4/3/3$ kilonovae ($\sim1/1/1/1$
afterglows) per year, respectively. The GW detection rates, GW population
properties, GW sky localizations, and optimistic ToO detection rates of
detectable EM counterparts for BNS GW events at the Advanced Plus, LIGO Voyager
and ET\&CE eras are detailedly simulated in this paper.
