We have performed a search for flares and quasi-periodic pulsations (QPPs) from low-mass M-dwarf stars using Transient Exoplanet Survey Satellite (TESS) two-minute cadence data. We find seven stars that show evidence of QPPs. Using Fourier and empirical mode decomposition techniques, we confirm the presence of 11 QPPs in these seven stars with a period between 10.2 and 71.9 minutes, including an oscillation with strong drift in the period and a double-mode oscillation. The fraction of flares that showed QPPs (7%) is higher than other studies of stellar flares, but it is very similar to the fraction of solar C-class flares. Based on the stellar parameters taken from the TESS Input Catalog, we determine the lengths and magnetic-field strengths of the flare coronal loops using the period of the QPPs and various assumptions about the origin of the QPPs. We also use a scaling relationship based on flares from the Sun and solar-type stars and the observed energy, plus the duration of the flares, finding that the different approaches predict loop lengths that are consistent to within a factor of about two. We also discuss the flare frequency of the seven stars determining whether this could result in ozone depletion or abiogenesis in any orbiting exoplanet. Three of our stars have a sufficiently high rate of energetic flares, which are likely to cause abiogenesis. However, two of these stars are also in the range where ozone depletion is likely to occur. We speculate on the implications of the flare rates, loop lengths, and QPPs for life on potential exoplanets orbiting in their host star’s habitable zone.