Characterizing K2 Candidate Planetary Systems Orbiting Low-mass Stars. II. Planetary Systems Observed During Campaigns 1-7

We recently used near-infrared spectroscopy to improve the characterization of 76 low-mass stars around which K2 had detected 79 candidate transiting planets. 29 of these worlds were new discoveries that had 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 We also statistically validate 17 planets (7 of which were previously unpublished), confirm the earlier validation of 22 planets, and announce 17 newly discovered planet candidates.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 21 planets or planet candidates with radii smaller than 1.25 R-circle plus, 18 super-Earths (1.252 R-circle plus), 21 small Neptunes (24 R-circle plus), three large Neptunes (46 R-circle plus), and eight giant planets (> 6 R-circle plus). Most of these planets are highly irradiated, but EPIC 206209135.04 (K2-72e, 1.29(-0.13)(+0.14) R-circle plus, EPIC 211988320.01 (R-P = 2.86(-0.15)(+0.16)R(circle plus_)), and EPIC 212690867.01 (2.20(-0.18)(+0.19)R(circle plus)) 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 1.53 R-circle plus planet candidates (F-p less than or similar to 20 F (circle plus)) orbiting brighter stars (Ks < 11) that are well-suited for atmospheric investigations with the Hubble, Spitzer, and/or James Webb Space Telescopes. 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(-1). Accordingly, they are possible targets for radial velocity mass measurement with current facilities or the upcoming generation of red optical and near-infrared high-precision RV spectrographs.