  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 placed from modelling of the Kepler
light curves. We find that the size of the planets detectable by Kepler around
these small stars typically lie in the range 1 to 5 Earth radii within the
habitable regions (P$\le$10 days). We identify one candidate transit with a
period of 1.26 days that resembles the signal produced by a planet slightly
smaller than the Moon. However, our pixel by pixel analysis of the Kepler data
shows that the signal most likely arises from a background contaminating
eclipsing binary. For 11 of these objects reliable photometric periods shorter
than 7 days are derived, and are interpreted as rotational modulation of
magnetic cool spots. For 3 objects we find possible photometric periods longer
than 50 days that require confirmation. H$_\alpha$ emission measurements and
flare rates are used as a 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 from their level of
chromospheric activity.
