  The effect of hydrostatic pressure and partial Na substitution on the
normal-state properties and the superconducting transition temperature ($T_c$)
of K$_{1-x}$Na$_x$Fe$_2$As$_2$ single crystals were investigated. It was found
that a partial Na substitution leads to a deviation from the standard $T^2$
Fermi-liquid behavior in the temperature dependence of the normal-state
resistivity. It was demonstrated that non-Fermi liquid like behavior of the
resistivity for K$_{1-x}$Na$_{x}$Fe$_2$As$_2$ and some KFe$_2$As$_2$ samples
can be explained by disorder effect in the multiband system with rather
different quasiparticle effective masses. Concerning the superconducting state
our data support the presence of a shallow minimum around 2 GPa in the pressure
dependence of $T_c$ for stoichiometric KFe$_2$As$_2$. The analysis of $T_c$ in
the K$_{1-x}$Na$_{x}$Fe$_2$As$_2$ at pressures below 1.5 GPa showed, that the
reduction of $T_c$ with Na substitution follows the Abrikosov-Gor'kov law with
the critical temperature $T_{c0}$ of the clean system (without pair-breaking)
which linearly depends on the pressure. Our observations, also, suggest that
$T_c$ of K$_{1-x}$Na$_x$Fe$_2$As$_2$ is nearly independent of the lattice
compression produced by the Na substitution. Further, we theoretically analyzed
the behavior of the band structure under pressure within the generalized
gradient approximation (GGA). A qualitative agreement between the calculated
and the recently in de Haas-van Alphen experiments [T. Terashima et al.,
Phys.Rev.B89, 134520(2014)] measured pressure dependencies of the Fermi-surface
cross-sections has been found. These calculations, also, indicate that the
observed minimum around 2~GPa in the pressure dependence of $T_c$ may occur
without a change of the pairing symmetry.
