We study the dynamics of optically-induced nuclear spin polarization in a fluorine-doped ZnSe epilayer via time-resolved Kerr rotation. The nuclear polarization in the vicinity of a fluorine donor is induced by interaction with coherently precessing electron spins in a magnetic field applied in the Voigt geometry. It is detected by nuclei-induced changes in the electron spin coherence signal. This all-optical technique allows us to measure the longitudinal spin relaxation time T1 of the 77 Se isotope in a magnetic field range from 10 to 130 mT under illumination. We combine the optical technique with radio frequency methods to address the coherent spin dynamics of the nuclei and measure Rabi oscillations, Ramsey fringes and the nuclear spin echo. The inhomogeneous spin dephasing time T * 2 and the spin coherence time T2 of the 77 Se isotope are measured. While the T1 time is on the order of several milliseconds, the T2 time is several hundred microseconds. The experimentally determined condition T1 ≫ T2 verifies the validity of the classical model of nuclear spin cooling for describing the optically-induced nuclear spin polarization.