Perturbation expansion for the asymmetric single-orbital Anderson Hamiltonian is extended to the case with finite magnetic field, and the self-energy part of the $d$-electron Green function is calculated up to the second order in $u=\frac{U }{\ensuremath{\pi}\ensuremath{\Delta}}$ for arbitrary asymmetry $\ensuremath{\eta}=\frac{1}{2}+\frac{{\ensuremath{\epsilon}}_{d}}{U}$ and magnetic field $h$. Zero-temperature density of localized states ${\ensuremath{\rho}}_{d\ensuremath{\sigma}}(\ensuremath{\omega})$, magnetic moment $m$ and static spin susceptibility $\ensuremath{\chi}$, and low-temperature specific heat ${C}_{v}=\ensuremath{\gamma}T$ and magnetoresistance $D$ of a dilute alloy are evaluated within the ${u}^{2}$ approximation. Plausible arguments are given (which become exact in the symmetric case) that the higher-order terms do not change the qualitative features of our results. For large enough $u$ the many-body (MB) effects give rise to three different types of behavior, depending on the value of asymmetry: (i) spin-fluctuation behavior for $\ensuremath{\eta}<\frac{1}{2}$, with large fluctuations of the $d$-level magnetization; (ii) mixed-valence behavior for $\ensuremath{\eta}\ensuremath{\simeq}\frac{1}{2}$, with large fluctuations of the $d$-level occupation; (iii) essentially mean-field behavior for $\ensuremath{\eta}>\frac{1}{2}$, where the MB effects are negligible even for $u\ensuremath{\gg}1$. Thus both $\ensuremath{\chi}$ and $\ensuremath{\gamma}$ at $h=0$ are enhanced by the increase of $u$ for $\ensuremath{\eta}<\frac{1}{2}$, reduced for $\ensuremath{\eta}>\frac{1}{2}$, and practically unaffected at $\ensuremath{\eta}\ensuremath{\simeq}\frac{1}{2}$. As functions of $\ensuremath{\eta}$ for a fixed $u$, $\ensuremath{\chi}$ and $\ensuremath{\gamma}$ have a maximum at $\ensuremath{\eta}=0$ and decrease monotonously with increasing $\ensuremath{\eta}$, and do so more steeply the higher the $u$. For $h\ensuremath{\ne}0$ and $\ensuremath{\eta}\ensuremath{\le}\frac{1}{2}$, $\ensuremath{\chi}$ and $\ensuremath{\gamma}$ decrease monotonously with increasing $h$, the decrease being quicker for higher $u$ and slower for higher $\ensuremath{\eta}$. For $\ensuremath{\eta}>\frac{1}{2}$, both $\ensuremath{\chi}$ and $\ensuremath{\gamma}$ exhibit a broad maximum at medium $h$ values, which becomes better pronounced with increasing $u$. The low-T magnetoresistance $D={\ensuremath{-}D}_{0}[1\ensuremath{-}\frac{1}{3}{D}_{2}{(\frac{\ensuremath{\pi}{k}_{B}T}{\ensuremath{\Delta}})}^{2}]$ is negative, with ${D}_{0}\ensuremath{\propto}{h}^{2}$ for small $h$ and ${D}_{0}\ensuremath{\rightarrow}1$ for large $h$. ${D}_{2}$ has a maximum at $h=0$ and drops down quickly with increasing $h$. Both ${D}_{0}$ and ${D}_{2}$ are enhanced by $u$ for $\ensuremath{\eta}<\frac{1}{2}$ and reduced for $\ensuremath{\eta}>\frac{1}{2}$. In the low-$h$ limit and for $\ensuremath{\eta}<\frac{1}{2}$, $D$ assumes a universal form for $u\ensuremath{\gg}{u}_{c}$, with both low-$T$ and low-$h$ behavior scaled by the same characteristic temperature ${\ensuremath{\Theta}}_{m}$. The density of localized states at $T=h=0$ is single peaked for $u\ensuremath{\lesssim}{u}_{c}$ and triple peaked for $u\ensuremath{\gg}{u}_{c}$ if $\ensuremath{\eta}<\frac{1}{2}$, with ${u}_{c}$ increasing with $\ensuremath{\eta}$. For $\ensuremath{\eta}\ensuremath{\ge}\frac{1}{2}$ it is single peaked for any finite $u$. For $\ensuremath{\eta}<\frac{1}{2}$ and $u\ensuremath{\gg}{u}_{c}$ the increasing $h$ splits ${\ensuremath{\rho}}_{d\ensuremath{\uparrow}}$ and ${\ensuremath{\rho}}_{d\ensuremath{\downarrow}}$, suppresses the narrow MB central peak above ${T}_{h}$, and restores the "magnetic" Hartree-Fock situation above ${h}_{0}$. Both ${T}_{h}$ and ${h}_{0}$ increase with increasing $\ensuremath{\eta}$. For $u\ensuremath{\lesssim}{u}_{c}$, ${T}_{h}\ensuremath{\sim}{h}_{0}\ensuremath{\sim}\ensuremath{\Delta}$.