When excited over a periodic metamaterial lattice of gold nanoparticles (~ 100nm), localized plasmon resonances (LPR) can be coupled by a diffraction wave propagating along the array plane, which leads to a drastic narrowing of plasmon resonance lineshapes (down to a few nm full-width-at-half-maximum) and the generation of singularities of phase of reflected light. These phenomena look very promising for the improvement of performance of plasmonic biosensors, but conditions of implementation of such diffractively coupled plasmonic resonances, also referred to as plasmonic surface lattice resonances (PSLR), are not always compatible with biosensing arrangement implying the placement of the nanoparticles between a glass substrate and a sample medium (air, water). Here, we consider conditions of excitation and properties of PSLR over arrays of glass substrate-supported single and double Au nanoparticles (~ 100-200nm), arranged in a periodic metamaterial lattice, in direct and Attenuated Total Reflection (ATR) geometries, and assess their sensitivities to variations of refractive index (RI) of the adjacent sample dielectric medium. First, we identify medium (PSLR, PSLR for air and water, respectively) and substrate (PSLR) modes corresponding to the coupling of individual plasmon oscillations at medium- and substrate-related diffraction cut-off edges. We show that spectral sensitivity of medium modes to RI variations is determined by the lattice periodicity in both direct and ATR geometries (~ 320nm per RIU change in our case), while substrate mode demonstrates much lower sensitivity. We also show that phase sensitivity of PSLR can exceed 10 degrees of phase shift per RIU change and thus outperform the relevant parameter for all other plasmonic sensor counterparts. We finally demonstrate the applicability of surface lattice resonances in plasmonic metamaterial arrays to biosensing using standard streptavidin-biotin affinity model. Combining advantages of nanoscale architectures, including drastic concentration of electric field, possibility of manipulation at the nanoscale etc, and high phase and spectral sensitivities, PSLRs promise the advancement of current state-of-the-art plasmonic biosensing technology toward single molecule label-free detection.