A theoretical calculation is performed for the ultrafast spin dynamics in nickel using an exact diagonalization method. The present theory mainly focuses on the situation where the intrinsic charge and spin dynamics is probed by the nonlinear (magneto-)optical responses on the femtosecond time scale, i.e. optical second harmonic generation (SHG) and the nonlinear magneto-optical Ken effect (NOLIMOKE). It is found that the ultrafast charge and spin dynamics are observable on the time scale of 10 fs. The charge dynamics proceeds ahead of the spin dynamics, which indicates the existence of a spin memory time. The fast decay results from the loss of coherence in the initial excited state. Both the material specific and experimental parameters affect the dynamics. We find that the increase of exchange interaction accelerates mainly the spin dynamics rather than the charge dynamics. A reduction of the hopping integrals, such as present at interfaces, slows down the spin dynamics significantly. Furthermore, it is found that a spectrally broad excitation yields the intrinsic speed limit of the charge (SHG) and spin dynamics (NOLIMOKE) while a narrower width prolongs the dynamics. This magnetic interface dynamics should then become accessible to state-of-the-art time-resolved nonlinear-optical experiments.