  The jet compositions, central engines, and progenitors of gamma-ray bursts
(GRBs) remain open questions in GRB physics. Applying broadband observations,
including GRB prompt emission and afterglow properties derived from {\em Fermi}
and {\em Swift} data, as well as from Keck host-galaxy observations, we address
these questions for the peculiar, bright GRB 110731A. By using the pair-opacity
method, we derive $\Gamma_{0}>190$ during the prompt emission phase.
Alternatively, we derive $\Gamma_{0} \approx 580$ and $\Gamma_{0} \approx 154$
by invoking the early-afterglow phase within the homogeneous density and wind
cases, respectively. On the other hand, nondetection of a thermal component in
the spectra suggests that the prompt emission is likely powered by dissipation
of a Poynting-flux-dominated jet leading to synchrotron radiation in an
optically thin region. The nondetection of a jet break in the X-ray and optical
bands allows us to place a lower limit on the jet opening angle $\theta_{\rm
j}>5.5^{\circ}$. Within a millisecond magnetar central engine scenario, we
derive the period $P_{0}$ and polar magnetic field strength $B_{\rm p}$, which
have extreme (but still allowed) values. The moderately short observed duration
(7.3\,s) and relatively large redshift ($z=2.83$) places the burst as a
"rest-frame short" GRB, so the progenitor of the burst is subject to debate.
Its relatively large $f_{{\rm eff}, z}$ parameter (ratio of the 1\,s peak flux
of a pseudo-GRB and the background flux) and a large physical offset from a
potential host galaxy suggest that the progenitor of GRB 110731A may be a
compact-star merger.
