  We investigate the ultraviolet (UV) spectral properties of faint
Lyman-$\alpha$ emitters (LAEs) in the redshift range 2.9<z<4.6 and provide
material to prepare future observations of the faint Universe. We use data from
the MUSE Hubble Ultra Deep Survey to construct mean rest-frame spectra of
continuum-faint (median M$_{UV}$ of -18 and down to M$_{UV}$ of -16), low
stellar mass (median value of $10^{8.4}$ and down to $10^{7}M_{\odot}$) LAEs at
redshift z>3. We compute various averaged spectra of LAEs sub-sampled on the
basis of their observational (e.g., Ly$\alpha$ strength, UV magnitude and
spectral slope) and physical (e.g., stellar mass and star-formation rate)
properties. We search for UV spectral features other than Ly$\alpha$, such as
higher-ionization nebular emission lines and absorption features. We
successfully observe the OIII]1666 and CIII]909 collisionally excited emission
lines and the HeII1640 recombination feature, as well as the resonant CIV1550
doublet either in emission or P-Cygni. We compare the observed spectral
properties of the different mean spectra and find the emission lines to vary
with the observational and physical properties of the LAEs. In particular, the
mean spectra of LAEs with larger Ly$\alpha$ equivalent widths, fainter UV
magnitudes, bluer UV spectral slopes and lower stellar masses show the
strongest nebular emission. The line ratios of these lines are similar to those
measured in the spectra of local metal-poor galaxies, while their equivalent
widths are weaker compared to the handful of extreme values detected in
individual spectra of z>2 galaxies. This suggests that weak UV features are
likely ubiquitous in high z, low-mass and faint LAEs. We publicly release the
stacked spectra as they can serve as empirical templates for the design of
future observations, such as those with the James Webb Space Telescope and the
Extremely Large Telescope.
