  We analyze the perturbative and parametric stability of the QCD predictions
for the Callan-Gross ratio $R(x,Q^2)=F_L/F_T$ and azimuthal $\cos(2\varphi)$
asymmetry in heavy-quark leptoproduction. Our analysis shows that large
radiative corrections to the structure functions cancel each other in their
ratio $R(x,Q^2)$ and azimuthal asymmetry with good accuracy. As a result, the
NLO contributions to the Callan-Gross ratio and $\cos(2\varphi)$ asymmetry are
less than 10% in a wide region of the variables $x$ and $Q^2$. We provide
compact analytic predictions for $R(x,Q^2)$ and asymmetry in the case of low
$x\ll 1$. Simple formulae connecting the high-energy behavior of the
Callan-Gross ratio and azimuthal asymmetry with the low-$x$ asymptotics of the
gluon density in the target are derived. It is shown that the obtained
hadron-level predictions for $R(x,Q^2)$ and azimuthal asymmetry are stable at
$x\ll 1$ under the DGLAP evolution of the gluon distribution function.
Concerning the experimental aspects, we propose to exploit the observed
perturbative stability of the Callan-Gross ratio and $\cos(2\varphi)$ asymmetry
in the extraction of the structure functions from the corresponding reduced
cross sections. In particular, our obtained analytic expressions simplify
essentially the determination of $F_2^c(x,Q^2)$ and $F_2^b(x,Q^2)$ from
available data of the H1 Collaboration. Our results will also be useful in
extraction of the azimuthal asymmetries from the incoming and future data on
heavy-quark leptoproduction.
