Observations of very low-mass stars with Kepler represent an excellent opportunity to search for planetary transits and to characterize optical photometric variability at the cool end of the stellar mass distribution. In this paper, we present low-resolution red optical spectra that allow us to identify 18 very low-mass stars that have Kepler light curves available in the public archive. Spectral types of these targets are found to lie in the range dM4.5-dM8.5, implying spectrophotometric distances from 17 pc to 80 pc. Limits to the presence of transiting planets are set by modeling of the Kepler light curves. We find that the size of the planets detectable by Kepler around these small stars typically lies in the range 1 to 5 Earth radii within the habitable regions (P ≤ 10 days). We identify one candidate transit with a period of 1.26 days whose light curve resembles a planet slightly smaller than the Moon. However, our pixel by pixel analysis of the Kepler data shows that the signal most likely arises from a background contaminating eclipsing binary. For 11 of these objects reliable photometric periods shorter than 7 days are derived, and are interpreted as rotational modulation of magnetic cool spots. For 3 objects we find possible photometric periods longer than 50 days that require confirmation. The Hα emission measurements and flare rates are used as proxies for chromospheric activity, and transversal velocities are used as an indicator of dynamical ages. These data allow us to discuss the relationship between magnetic activity and detectability of planetary transits around very low-mass stars. We show that super-Earth planets with sizes around 2 Earth radii are detectable with Kepler around about two thirds of the stars in our sample, independently of their level of chromospheric activity.