We present the analysis of new NIR, intermediate-resolution spectra of the gravitationally lensed galaxy the 8 oclock 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 oclock 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 oclock 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)
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