We recently used near-infrared spectroscopy to improve the characterization of 76 low-mass stars around which K2 had detected 79 candidate transiting planets. Thirty of these worlds were new discoveries that have not previously been published. We calculate the false positive probabilities that the transit-like signals are actually caused by non-planetary astrophysical phenomena and reject five new transit-like events and three previously reported events as false positives. We also statistically validate 18 planets (eight of which were previously unpublished), confirm the earlier validation of 21 planets, and announce 17 newly discovered planet candidates. Revising the properties of the associated planet candidates based on the updated host star characteristics and refitting the transit photometry, we find that our sample contains 20 planets or planet candidates with radii smaller than 1.25 Earth radii, 20 super-Earths (1.25-2 Earth radii), 20 small Neptunes (2-4 Earth radii), three large Neptunes (4-6 Earth radii), and eight giant planets (> 6 Earth radii). Most of these planets are highly irradiated, but EPIC 206209135.04 (K2-72e, Rp = 1.29 (-0.13/+0.14) Earth radii), EPIC 211988320.01 (Rp = 2.86 (-0.15/+0.16) Earth radii), and EPIC 212690867.01 (Rp = 2.20 (-0.18/+0.19) Earth radii) orbit within optimistic habitable zone boundaries set by the recent Venus inner limit and the early Mars outer limit. In total, our planet sample includes eight moderately-irradiated 1.5-3 Earth radius planet candidates (Fp < 20 F_Earth) orbiting brighter stars (Ks < 11) that are well-suited for atmospheric investigations with Hubble, Spitzer, and/or the James Webb Space Telescope. Five validated planets orbit relatively bright stars (Kp < 12.5) and are expected to yield radial velocity semi-amplitudes of at least 2 m/s.
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