The halo of M31 shows a wealth of substructures, some of which are consistent with assembly from satellite accretion. Here we report on kinematic and abundance results from Keck DEIMOS spectroscopy in the near-infrared calcium triplet region of over 3500 red giant star candidates along the minor axis and in off-axis spheroid fields of M31. These data reach out to large radial distances of about 160 kpc. The derived radial velocity distributions show an indication of a kinematically cold substructure around ~17 kpc, which has been reported before. We devise a new and improved method to measure spectroscopic metallicities from the calcium triplet in low signal-to-noise ratio spectra using a weighted co-addition of the individual lines. The resulting distribution (accurate to ~0.3 dex down to signal-to-noise ratios of 5) leads us to note an even stronger gradient in the abundance distribution along M31's minor axis and in particular toward the outer halo fields than previously detected. The mean metallicity in the outer fields reaches below -2 dex, with individual values as low as lesssim-2.6 dex. This is the first time such a metal-poor halo has been detected in M31. In the fields toward the inner spheroid, we find a sharp decline of ~0.5 dex in metallicity in a region at ~20 kpc, which roughly coincides with the edge of an extended disk, previously detected from star count maps. A large fraction of red giants that we detect in the most distant fields are likely members of M33's overlapping halo. A comparison of our velocities with those predicted by new N-body simulations argues that the event responsible for the Giant Stream is most likely not responsible for the full population of the inner halo. We show further that the abundance distribution of the Stream is different from that of the inner halo, from which it becomes evident, in turn, that the merger event that formed the Stream and the outer halo cannot have contributed any significant material to the inner spheroid. All these severe structure changes in the halo suggest a high degree of infall and stochastic abundance accretion governing the buildup of M31's inner and outer halo.Some of the data presented herein were obtained at the W. M. Keck Observatory, which is operated as a scientific partnership among the California Institute of Technology, the University of California, and the National Aeronautics and Space Administration. The Observatory was made possible by the generous financial support of the W. M. Keck Foundation.