Using 3D high-resolution hydrodynamic simulations, tracking both electrons and ions, we study the effects of turbulence and conduction in the hot intracluster medium. We show how the power spectrum of the gas density perturbations can accurately constrain both processes. The characteristic amplitude of density perturbations is linearly related to the strength of turbulence, i.e. the 3D Mach number, as A(k)_max = 0.25 M. The slope of A(k) in turn reflects the level of conduction. In a non-conductive medium, subsonic stirring motions advect density with a similar nearly Kolmogorov cascade. Increasing conduction (via magnetic suppression f = 0.001-1) progressively steepens the spectrum towards the Burgers-like regime. The turbulent Prandtl number defines the dynamic similarity of the flow; at scales where Pt 0.1), Pt ~ 100 occurs on spatial scales larger than the injection scale. The velocity spectrum is instead not much affected by conduction. The f > 0.1 regime affects the appearance of X-ray images, in which Kelvin-Helmholtz and Rayleigh-Taylor rolls and filaments are washed out. In a stratified system, weak/strong turbulence induces higher isobaric/adiabatic fluctuations, while conduction forces both modes towards the intermediate isothermal regime. We provide a general analytic fit which is applied to new deep Chandra observations of Coma. The observed spectrum is best consistent with strongly suppressed effective isotropic conduction, f = 0.001, and mild subsonic turbulence, M = 0.45 (with injection at ~250 kpc). The low conductivity corroborates the survival of sharp features in the ICM (cold fronts, filaments, bubbles), and indicates that cooling flows may not be balanced by conduction. ; Comment: Accepted by A&A - added several insights and comments; 17 pages, 11 figures