  The recent observation of GW190412, the first high-mass ratio binary
black-hole (BBH) merger, by the LIGO-Virgo Collaboration (LVC) provides a
unique opportunity to probe the impact of subdominant harmonics and precession
effects encoded in a gravitational wave signal. We present refined estimates of
source parameters for GW190412 using \texttt{NRSur7dq4}, a recently developed
numerical relativity waveform surrogate model that includes all $\ell \leq 4$
spin-weighted spherical harmonic modes as well as the full physical effects of
precession. We compare our results with two different variants of
phenomenological precessing BBH waveform models, \texttt{IMRPhenomPv3HM} and
\texttt{IMRPhenomXPHM}, as well as to the LVC results. Our results are broadly
in agreement with \texttt{IMRPhenomXPHM} results and the reported LVC analysis
compiled with the \texttt{SEOBNRv4PHM} waveform model, but in tension with
\texttt{IMRPhenomPv3HM}. Using the \texttt{NRSur7dq4} model, we provide a
tighter constraint on the mass-ratio ($0.26^{+0.08}_{-0.06}$) as compared to
the LVC estimate of $0.28^{+0.13}_{-0.07}$ (both reported as median values
withs 90\% credible intervals). We also constrain the binary to be more
face-on, and find a broader posterior for the spin precession parameter. We
further find that even though $\ell=4$ harmonic modes have negligible
signal-to-noise ratio, omission of these modes will influence the estimated
posterior distribution of several source parameters including chirp mass,
effective inspiral spin, luminosity distance, and inclination. We also find
that commonly used model approximations, such as neglecting the asymmetric
modes (which are generically excited during precession), have negligible impact
on parameter recovery for moderate SNR-events similar to GW190412.
