We study the perturbative and parametric stability of the QCD predictions for the Callan-Gross ratio $R(x,Q^2)=F_L/F_T$ and azimuthal $cos(2varphi)$ asymmetry, $A(x,Q^2)$, in heavy-quark leptoproduction. We review the available theoretical results for these quantities and conclude that, contrary to the production cross sections, the ratios $R(x,Q^2)$ and $A(x,Q^2)$ are stable under radiative QCD corrections in wide region of the variables $x$ and $Q^2$. This implies that large radiative contributions to the structure functions cancel each other in the ratios $R(x,Q^2)$ and $A(x,Q^2)$ with good accuracy. Then we consider some experimental and phenomenological applications of the observed perturbative stability. We provide compact analytic predictions for $R(x,Q^2)$ and azimuthal $cos(2varphi)$ asymmetry in the case of low $xll 1$. It is demonstrated that our obtained results will be useful in the extraction of the structure functions from measurements of the reduced cross sections. Finally, we analyze the properties of $R(x,Q^2)$ and $A(x,Q^2)$ within the variable-flavor-number scheme (VFNS) of QCD. We conclude that the Callan-Gross ratio and azimuthal asymmetry are perturbatively stable but sensitive to resummation of the mass logarithms of the type $alpha_{s}lnleft( Q^{2}/m^{2}right)$. For this reason, the quantities $R(x,Q^2)$ and $A(x,Q^2)$ will be good probes of the heavy-quark content of the proton.
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