This review paper is aimed at studying the problems as follows: (1) the Widom line and its analogues in supercooled and supercritical regions; (2) effects of dimensional crossover (DC) on the critical exponents, effective spatial d_(eff) and fractal d_(fr) dimensionalities; (3) anomalous behavior of the diffusion coefficient D and the shear viscosity coefficientηin bulk fluids and confined supercooled water (CSW) near the critical points; (4) spectra of the light molecular scattering (LMS) and quasi-elastic neutron scattering (QENS) and its possible medical applications. The effective critical exponents as well as the effective spatial d_(eff) and fractal d_(fr) dimensionalities were calculated for confined fluids like CSW. A3d ?2d DC between the critical exponents α= 0,β=1/8,δ=15,γ=7/4,v=1 and α= 0.110,β= 0.3265, δ= 4.789,γ=1.237,v=0.630 for 2d and 3d systems belonging to the Ising-model universality class were taken into account. Anomalies of the diffusion coefficient were examined in bulk water and CSW in wide intervals of the size and thermodynamic variables corresponding to crossover phenomena between the dynamic fluctuation, crossover and regular regions. The transition between dynamic crossover and regular regions in bulk fluids, including bulk water, is illustrated by changes in the diffusion-coefficient dependences on: (a) the size variable-from D~ L~(-1.963) to D~ L~(-2), (b) the temperature variable-from D~ (T - Tc)~(1. 237) to D~ (T - Tc), (c) the concentration variable-from D~ (x - x_c)~(3.789) to D~ (x - x_c)~2, (d) the pressure variable D~ (p - p_c)~(0.791) to D~ (p - Pc)~(0.667.) In confined 2d fluids like CSW such a transition between crossover and regular behaviors should be treated as 2d? 4d crossover phenomena because results of the Landau mean-field theory are valid for d= 4 (with a logarithmic accuracy). A 2d ? 4d crossover leads to the following changes in dependence of the diffusion coefficient D on: (a) the size variable from D~ L~(
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