To characterize the absorption properties of this circumgalactic medium (CGM) and its relation to the LG we present the so-far largest survey of metal absorption in Galactic high-velocity clouds (HVCs) using archival ultraviolet (UV) spectra of extragalactic background sources. The UV data are obtained with the Cosmic Origins Spectrograph (COS) onboard the Hubble Space Telescope (HST) and are supplemented by 21 cm radio observations of neutral hydrogen. Along 270 sightlines we measure metal absorption in the lines of SiII, SiIII, CII, and CIV and associated HI 21 cm emission in HVCs in the velocity range |v_LSR|=100-500 km s^-1. With this unprecedented large HVC sample we were able to improve the statistics on HVC covering fractions, ionization conditions, small-scale structure, CGM mass, and inflow rate. For the first time, we determine robustly the angular two point correlation function of the high-velocity absorbers, systematically analyze antipodal sightlines on the celestial sphere, and compare the absorption characteristics with that of Damped Lyman alpha absorbers (DLAs) and constrained cosmological simulations of the LG. Our study demonstrates that the Milky Way CGM contains sufficient gaseous material to maintain the Galactic star-formation rate at its current level. We show that the CGM is composed of discrete gaseous structures that exhibit a large-scale kinematics together with small-scale variations in physical conditions. The Magellanic Stream clearly dominates both the cross section and mass flow of high-velocity gas in the Milky Ways CGM. The possible presence of high-velocity LG gas underlines the important role of the local cosmological environment in the large-scale gas-circulation processes in and around the Milky Way (abridged).