Data on elastic scattering of 96 MeV neutrons from 56Fe, 89Y and 208Pb in the angular interval 10-70° are presented. The previously published data on 208Pb have been extended, as a new method has been developed to obtain additional information at the most forward angles. The results are compared with phenomenological and microscopic optical potentials. The theory predictions are in general in good agreement with the experimental data. A study of the deviation of the zero-degree cross section from Wick's limit has been performed. The data on 208Pb are in agreement with Wick's limit, while those on lighter nuclei overshoot the limit significantly. A novel analysis method has been developed to obtain the inelastic neutron emission cross sections from the existing 56Fe data. The method is based on folding a trial spectrum with the response of the detector setup. The data cover the angular interval 26-65° and an excitation energy range of 0-45 MeV, ranges hitherto not studied. The results are compared with nuclear model predictions and found to be in good agreement with the experimental data.