Context. Galaxy evolution and star formation are two multi-scale problems tightly linked to each other. Aims. We aim to describe simultaneously the large-scale evolution widely induced by the feedback processes and the details of the gas dynamics that controls the star formation process through gravitational collapse. This is a necessary step in understanding the interstellar cycle, which triggers galaxy evolution. Methods. We performed a set of three-dimensional high-resolution numerical simulations of a turbulent, self-gravitating and magnetized interstellar medium within a 1 kpc stratified box with supernova feedback correlated with star-forming regions. In particular, we focussed on the role played by the magnetic field and the feedback on the galactic vertical structure, the star formation rate (SFR) and the flow dynamics. For this purpose we have varied their respective intensities. We extracted properties of the dense clouds arising from the turbulent motions and compute power spectra of various quantities. Results. Using a distribution of supernovae sufficiently correlated with the dense gas, we find that supernova explosions can reproduce the observed SFR, particularly if the magnetic field is on the order of a few µG. The vertical structure, which results from a dynamical and an energy equilibrium is well reproduced by a simple analytical model, which allows us to roughly estimate the efficiency of the supernovae in driving the turbulence in the disc to be rather low, of the order of 1.5%. Strong magnetic fields may help to increase this efficiency by a factor of between two and three. To characterize the flow we compute the power spectra of various quantities in 3D but also in 2D in order to account for the stratification of the galactic disc. We find that within our setup, the compressive modes tend to dominate in the equatorial plane, while at about one scale height above it, solenoidal modes become dominant. We measured the angle between the magnetic and velocity fields and we conclude that they tend to be well aligned particularly at high magnetization and lower feedback. Finally, the dense structures present scaling relations that are reminiscent of the observational ones. The virial parameter is typically larger than 10 and shows a large spread of masses below 1000 M . For masses larger than 10 4 M , its value tends to a few. Conclusions. Using a relatively simple scheme for the supernova feedback, which is self-consistently proportional to the SFR and spatially correlated to the star formation process, we reproduce a stratified galactic disc that presents reasonable scale height, SFR as well as a cloud distribution with characteristics close to the observed ones.