Stars play a central role in modern astrophysics. To understand how stars form is therefore fundamental for the field. Stars form in gas clouds in the interstellar medium. This medium is magnetized and turbulent; star formation is therefore a complex, highly non-linear and multiscale problem. In this context, star formation processes are still not well-known, and particularly protostellar disk and multiple stars -- which means stars that are gravitationaly bound -- formation. Numerical simulations are crucial to have a better insight of these processes. This work is divided in two main parts, dedicated to the study of the first phases of star formation. The first part presents the numerical simulations I performed during my thesis to invest...