We consider the screening of the negative charges (carboxylic acid groups) fixed on the surface of a conical-shaped track-etched nanopore by divalent magnesium (Mg2+) and trivalent lanthanum (La3+). The experimental current (I)-voltage (V) curves and current rectification ratios allow discussing fundamental questions about the overcompensation of spatially-fixed charges by multivalent ions over nanoscale volumes. The effects of charge inversion or reversal on nanopore transport are discussed in mixtures of asymmetric electrolytes (LaCl3 and MgCl2 with KCl). In particular, pore charge inversion is demonstrated for La3+ as well as for mixtures of this trivalent ion at low concentrations with monovalent potassium (K+) and divalent Mg2+ ions at biologically relevant concentrations. It is found that small concentrations of multivalent ions can modulate the nanopore rectification and the transport of other majority ions in the solution. We study also the kinetics of the nanopore electrical recovery when the electrolyte solutions bathing the single-pore membrane are changed and show the hysteretic effects observed in the I-V curves. Finally, we describe the hysteresis observed in the I-V curves of CaCl2, MgCl2, and BaCl2 and mixtures. We also give a qualitative description of the effects of charge reversal on the pore rectification using the Nernst-Planck flux equations for multivalent ion mixtures.