Phase conjugation and amplification of linear and nonlinear magnetostatic waves (MSW) in yttrium iron garnet (YIG) films has been investigated both experimentally and theoretically. The experiment was performed using parametric pumping localized in area with lengths from the values less than MSW's wavelength to the values appreciably more than length of MSW's free path. The inversion ratio (up to 35 dB) of conjugated wave and amplification ratio (up to 40 dB) of transmitted wave have been measured for different values of pumping area length, pumping power and duration, and other parameters. The theory of interaction of MSW with localized nonstationary parametric electromagnetic pumping was developed. The calculated data show good agreement with experimental ones. New method of direct measurement of MSW's relaxation time based on the phase conjugation technique is proposed. At first time the inversion of the shape of complicated input signal has been realized in real-time scale. Extremely large amplification ratio (17 dB) of magnetostatic envelope soliton has been obtained experimentally, and the theoretical explanation of this phenomenon is proposed.