  We present the analysis of new NIR, intermediate-resolution spectra of the
gravitationally lensed galaxy "the 8 o'clock arc" at z_sys = 2.7350 obtained
with VLT/X-shooter. These rest-frame optical data, combined with HST and
Spitzer images, provide very valuable information, which nicely complement our
previous detailed rest-frame UV spectral analysis. From high-resolution HST
images, we reconstruct the morphology of the arc in the source plane, and
identify that the source is formed of two majors parts, the main galaxy
component and a smaller blob separated by 1.2 kpc in projected distance. The
blob, with a twice larger magnification factor, is resolved in the spectra. The
multi-Gaussian fitting of detected nebular emission lines and the spectral
energy distribution modeling of the available multi-wavelength photometry
provide the census of gaseous and stellar dust extinctions, gas-phase
metallicities, star-formation rates (SFRs), and stellar, gas, and dynamical
masses for both the main galaxy and the blob. As a result, the 8 o'clock arc
shows a marginal trend for a more attenuated ionized gas than stars, and
supports a dependence of the dust properties on the SFR. With a high specific
star-formation rate, SSFR = 33+/-19 Gyr^{-1}, this lensed Lyman-break galaxy
deviates from the mass-SFR relation, and is characterized by a young age of
40^{+25}_{-20} Myr and a high gas fraction of about 72%. The 8 o'clock arc
satisfies the fundamental mass, SFR, and metallicity relation, and favors that
it holds up beyond z~2.5. We believe that the blob, with a gas mass M_gas =
(2.2+/-0.9)x10^{9} Msun (one order of magnitude lower than the mass of the
galaxy), a half-light radius r1/2 = 0.53+/-0.05 kpc, a star-formation rate
SFR_Halpha = 33+/-19 Msun yr^{-1}, and in rotation around the main core of the
galaxy, is one of these star-forming clumps commonly observed in z>1
star-forming galaxies. (Abridged)
