We use optical integral field spectroscopy from VLT/MUSE, as well as photometric observations from Hubble Space Telescope and VLT/HAWK-I, to study the morpho-kinematics of 17 low mass (log(M/M ) < 9.5) MACS J0416.1-2403 cluster galaxies at R 200 and 5 field galaxies with a redshift of z ∼0.4. By measuring fluxes of strong emission lines from the MUSE data, we have recovered the star formation rates, gas-phase metallicities, spatially resolved gas kinematics and also investigated the ionising mechanisms. We have analysed the structure and morphology of the galaxies from the optical and infrared photometric data, performing a multi-component decomposition into a bulge and a disk. The spatially resolved gas velocity fields of the cluster members and field galaxies were modelled using a 3D approach, which allowed us to retrieve their intrinsic gas kinematics, including the maximum rotation velocity and velocity dispersion. This enabled us to study scaling relations such as the Tully-Fisher and the stellar mass -S 0.5 relation for low mass galaxies in different environments and to search for signatures of cluster-specific processes using disturbed gas velocity fields as tracers. Most galaxies from our sample fall in the star forming and composite region in the BPT diagnostic diagram, which allows the ionising sources in a galaxy to be disentangled. The cluster and field population can be classified as star forming main-sequence galaxies, with only a sub-sample of four quenched systems. We observe significant scatter for the cluster galaxies in the mass-metallicity plane, and the lowest mass systems deviate from the predictions of the fundamental metallicity relation, showing higher metallicities, whereas the higher mass ones are in accordance with the model predictions. This might hint at the cut-off of pristine gas inflow and/or the removal of the hot halo gas as the mechanisms driving these offsets. Our morpho-kinematic analysis reveals a sub-sample of dwarfs with maximum velocities v max <50 km/s and v max, gas /σ gas < 1, which depart from the Tully-Fisher relation. This might indicate that their interstellar medium is affected by external environmental processes, such as RPS. However, ∼ 30% of the cluster galaxies have rotation-dominated gas disks and follow the Tully-Fisher relation within 1σ. Using the S 0.5 parameter, which links the dynamical support of ordered motions with that of random motions, we can separate between galaxies affected by gravitational processes and hydrodynamical ones. In the stellar mass -S 0.5 plane, both cluster and field galaxies follow a tight sequence, with only a sub-population of 5 galaxies strongly departing (> 4σ) from this relation, showing high σ gas values. Both the morphology and kinematics of the outlier galaxies hint at a combination of pre-processing and cluster-specific interactions affecting their stellar and gas disks. Thus, in our sample of low-mass galaxies in a rich cluster at z ∼ 0.4, 65% exhibit disordered motions in their velocity fields, in contrast to previous ...