  We present the infrared (IR) and X-ray properties of a sample of 33 mid-IR
luminous quasars ($\nu$L(6 micron)>6x10$^{44}$ erg/s) at redshift z~1-3,
identified through detailed spectral energy distribution analyses of distant
star-forming galaxies, using the deepest IR data from Spitzer and Herschel in
the GOODS-Herschel fields. The aim is to constrain the fraction of obscured,
and Compton-thick (CT, N$_H$>1.5x10$^{24}$ cm$^{-2}$) quasars at the peak era
of nuclear and star-formation activities. Despite being very bright in the
mid-IR band, ~30% of these quasars are not detected in the extremely deep 2 Ms
and 4 Ms Chandra X-ray data available in these fields. X-ray spectral analysis
of the detected sources reveals that the majority (~67%) are obscured by column
densities N$_H$>10$^{22}$ cm$^{-2}$; this fraction reaches ~80% when including
the X-ray undetected sources (9 out of 33), which are likely to be the most
heavily-obscured, CT quasars. We constrain the fraction of CT quasars in our
sample to be ~24-48%, and their space density to be
$\Phi$=(6.7$\pm$2.2)x10$^{-6}$ Mpc$^{-3}$. From the investigation of the quasar
host galaxies in terms of star-formation rates (SFRs) and morphological
distortions, as a sign of galaxy mergers/interactions, we do not find any
direct relation between SFRs and quasar luminosity or X-ray obscuration. On the
other hand, there is tentative evidence that the most heavily-obscured quasars
have, on average, more disturbed morphologies than the
unobscured/moderately-obscured quasar hosts, which preferentially live in
undisturbed systems. However, the fraction of quasars with disturbed morphology
amongst the whole sample is ~40%, suggesting that galaxy mergers are not the
main fuelling mechanism of quasars at z~2.
