More than 4000 exoplanets have been discovered to date, providing the search for a place capable of hosting life with a large number of targets. With the Transiting Exoplanet Survey Satellite (TESS) having completed its primary mission in July 2020, the number of planets confirmed by follow-up observations is growing further. Crucial for planetary habitability is not only a suitable distance of the planet to its host star, but also the star's properties. Stellar magnetic activity, and especially flare events, expose planets to a high photon flux and potentially erode their atmospheres. Here especially the poorly constrained high-energy UV and X-ray domain is relevant. We characterize the magnetic activity of M dwarfs to provide the planet community with information on the energy input from the star; in particular, next to the frequency of optical flares directly observed with TESS we aim at estimating the corresponding X-ray flare frequencies making use of the small pool of known events observed simultaneously in both wavebands. We identified 112 M dwarfs with a TESS magnitude <=11.5 for which TESS can probe the full habitable zone for transits. These 112 stars have 1276 two-minute cadence TESS light curves from the primary mission which we searched for rotational modulation and flares. We study the link between rotation and flares and between flare properties, e.g. the flare amplitude-duration relation and cumulative flare energy frequency distributions (FFDs). Assuming that each optical flare is associated to a flare in the X-ray band, and making use of published simultaneous Kepler/K2 and XMM-Newton flare studies, we estimate the X-ray energy released by our detected TESS flare events. Our calibration involves also the relation between flare energies in the TESS and K2 band. We detected more than 2500 optical flare events on a fraction of about 32% of our targets and found reliable rotation periods only for 12 stars which is a fraction of about 11%. For these 12 targets, we present cumulative flare energy frequency distributions (FFDs) and FFD power law fits. We construct FFDs in the X-ray band by calibrating optical flare energies to the X-rays. In the absence of directly observed X-ray FFDs for main-sequence stars, our predictions can serve for estimates of the high-energy input to the planet of a typical fast-rotating early- or mid-M dwarf.