  In spite of their conjectured importance for the Epoch of Reionization, the
properties of low-mass galaxies are currently still under large debate. In this
article, we study the stellar and gaseous properties of faint, low-mass
galaxies at z>3. We observed the Frontier Fields cluster Abell S1063 with MUSE
over a 2 arcmin^2 field, and combined integral-field spectroscopy with
gravitational lensing to perform a blind search for intrinsically faint Lya
emitters (LAEs). We determined in total the redshift of 172 galaxies of which
14 are lensed LAEs at z=3-6.1. We increased the number of
spectroscopically-confirmed multiple-image families from 6 to 17 and updated
our gravitational-lensing model accordingly. The lensing-corrected Lya
luminosities are with L(Lya) <= 10^41.5 erg/s among the lowest for
spectroscopically confirmed LAEs at any redshift. We used expanding gaseous
shell models to fit the Lya line profile, and find low column densities and
expansion velocities. This is to our knowledge the first time that gaseous
properties of such faint galaxies at z>=3 are reported. We performed SED
modelling to broadband photometry from the U-band through the infrared to
determine the stellar properties of these LAEs. The stellar masses are very low
(10^{6-8} Msun), and are accompanied by very young ages of 1-100 Myr. The very
high specific star formation rates (~100 Gyr^-1) are characteristic of
starburst galaxies. The UV-continuum slopes beta are low in our sample, with
beta<-2 for all galaxies with M_star<10^8 Msun. We conclude that our low-mass
galaxies at 3<z<6 are forming stars at higher rates when correcting for stellar
mass effects than seen locally or in more massive galaxies. The young stellar
populations with high star-formation rates and low HI column densities lead to
continuum slopes and LyC-escape fractions expected for a scenario where low
mass galaxies reionise the Universe.
