{\it Gaia} DR2 giants in the Galactic dust -- I. Reddening across the whole dust layer and some properties of the giant clump

We consider a complete sample of 101810 giants with Gaia DR2 parallaxes $\varpi$ within the red clump domain of the Hertzsprung-Russell diagram in the space cylinder with a radius of 700 pc around the Sun and a height of $\mathrm{\mid }Z\mathrm{\mid }=1800$ pc. We use the Gaia DR2 $G_{\mathrm{B}\mathrm{P}}$, $G_{\mathrm{R}\mathrm{P}}$ and WISE $W3$ photometry. We describe the spatial variations of the modes of the observables $G_{\mathrm{B}\mathrm{P}}-G_{\mathrm{R}\mathrm{P}}$, $G_{\mathrm{R}\mathrm{P}}-W3$, $G_{\mathrm{B}\mathrm{P}}+5+5{\log }_{10}\varpi$, $G_{\mathrm{R}\mathrm{P}}+5+5{\log }_{10}\varpi$, and $W3+5+5{\log }_{10}\varpi$ by extinction and reddening in combination with linear vertical gradients of the intrinsic colours and absolute magnitudes of the red giant clump. The derived clump median absolute magnitude in $W3$ agrees with its recent literature estimates. The clump median intrinsic colours and absolute magnitudes in $G_{\mathrm{B}\mathrm{P}}$ and $G_{\mathrm{R}\mathrm{P}}$ are derived for the first time at a precision level of 0.01 mag. We confirm the reliability of the derived clump absolute magnitudes, intrinsic colours, and their vertical gradients by comparing them with the theoretical predictions from PARSEC, MIST and BaSTI isochrones. This leads us to the median age and [Fe/H] of the clump within $\mathrm{\mid }Z\mathrm{\mid }<1.7$ kpc from the Galactic mid-plane as $(2.3\pm 0.5)+(3.2\pm 1.6)\mathrm{\mid }Z\mathrm{\mid }$ Gyr and $(-0.08\pm 0.08)-(0.16\pm 0.07)\mathrm{\mid }Z\mathrm{\mid }$ dex, respectively, where $Z$ is expressed in kpc. These results agree with recent empirical and theoretical estimates. Moreover, all the models give similar age-metallicity relations by use of our results in the optical range. The derived extinctions and reddenings across the whole dust half-layer below or above the Sun converge to the reddening $E(B-V)=0.06$ mag by use of the most reliable extinction laws.