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 \mathrm { Ly } \alpha 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 \mathrm { Ly } \alpha luminosities are with L _ { \mathrm { Ly } \alpha } \lesssim 10 ^ { 41.5 } erg/s among the lowest for spectroscopically confirmed LAEs at any redshift . We used expanding gaseous shell models to fit the \mathrm { Ly } \alpha 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 \gtrsim 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 } M _ { \odot } ) , and are accompanied by very young ages of 1-100 Myr . The very high specific star formation rates ( \sim 100 Gyr ^ { -1 } ) are characteristic of starburst galaxies , and we find that most galaxies will double their stellar mass in \lesssim 20 Myr . The UV-continuum slopes \beta are low in our sample , with \beta < -2 for all galaxies with M _ { \star } < 10 ^ { 8 } M _ { \odot } . 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 H I column densities lead to continuum slopes and LyC-escape fractions expected for a scenario where low mass galaxies reionise the Universe .