The electronic structure of rare-earth $4f$-metals (REM) is calculated within the many-electron operator spinors (MEOS) representation. Localized $4f$-electrons (MEOS $F_r^n$ , $n=1-7$) have spin $S_r$ (MEOS spin factor is $c_{rS\sigma}$) and orbital moment $L_r$ (MEOS factor is $\nu_{rL}$). The $5d$-electrons exited on covalent bonds (MEOS is $D_r = \{d_{r\sigma l} c_{rS\sigma} \nu_{rL}\}$) with amplitude $\xi_D$ of wave function create the $4f$—$5d$—$4f$ exchange between ions. Localization conditions ($d_r \overline{d_r} = 1 = F_r \overline{F_r}$) define MEOS and their secondary quantization by the Bogolyubov Green functions’ method. Spontaneous magnetization, $M_s$, and ferromagnetic anisotropy (FMA) are expressed through the angular moment $J_r$ (or $J_T = \langle J_r^z \rangle $). The small value of $T_c (T_N) \cong 10^2$ K for heavy REM (except Gd) is defined by unfreezing of $s_r$, $l_r$ and $\xi_D^2 \ll 1$ of covalent $5d$-electrons. Their chemical bond fluctuations (CBF) $E_k^D = \Gamma k^2$ decrease magnon energy $E_k^m = 2AJk^2 + \mu(B_A + B)$ by $\Delta E^m = -\Delta Ak$ ($\Delta A \propto T^2$). FMA field ($B_A > 0$) stabilizes FM phase at $T < T_{0c} \cong 10^2$ K. When $T > T_{0c}$, the nonmonotonic $E^m(k)$ function changes its sign at $k = k_0 = Q_c \propto (T - T_{0c})$. Destabilized FM phase transforms in helicoid with vector $Q_c(T) \cong 0,1$ for Tb, Dy, Ho. Application of magnetic field, $B = B_c \propto (T - T_{0c}) \cong 1$ T, causes the first-kind metamagnetic transition into FM phase. Exchange integral, $A(S, L)$, is composed from spin and orbital parts owing to $s_r$ or $l_r$ unfreezing. Crystal field (CF) mechanism for FMA is calculated as repulsion of ‘effective charges’ ($\propto F_r \overline{D_r}$). H.C.P. deformation ($\propto u_{zz} \cong −10^{−2}$) of cubic lattice separates CF anisotropic parts ($\propto s_r^z S_r^z$ and $l_r^z L_r^z $). Their contributions into FMA constants ($K_1^{CF}, ...$) depend on the Hund exchange ($A_D$) and on the spin–orbit coupling, $\lambda$. Their expression through the Lande’s $g$-factor (at transition to ($J_r^z J_R^z$)) form) separates critical value $g = 5/4$. When $g < 5/4$, constant $K_1^{CF}$ ($> 0$ for Tb, Dy, Ho) changes its sign ($K_1^{CF} < 0$ for Er, Tm. The sign of experimental FMA constant ($K_1^{exp} = -(K_1^{CF} + 2K_2^{CF})$) changes accordingly. Analogous calculation of ferromagnetic magnetostriction (FMS) within the CF mechanism gives also large FMS parameters ($\Lambda \cong 10$ эрг/см$^3$) and their constants, $\hat{\lambda} \cong 10$. Anisotropy of ‘giant FMS’ of cubic TbFe$_2$ (and other analogous intermetallides) is explained by strong Fe–Tb–Fe bonds along [111] that gives $\lambda_{111} \ll |\lambda_{100}|$. Particular case is Gd ($n = 7$, $L = 0$, stable half-filled $4f$-shell). The CF contribution into FMA is small at weak sr and lr unfreezing. Competing contribution of covalent FMA term (of the same value, but opposite sign) with strong dependence on $T$ creates $K_1^{exp}(T)$ nonmonotony and complex MPD owing to screening effects. Large absorption of hydrogen in REM is explained by strong covalent Me–H bonds. MeH$_x$ system ($x > 1$) has strong dependence $x_0(T)$ in equilibrium ($x = x_0$) owing to CBF. Growth of electrical resistance, $R(x)$, with $x$ growth is explained by change of the Fermi surface near crossing of band spectrum with CBF. The linear part of its dispersion law, $\tilde{\varepsilon}(k) \propto k$, appears. DOS($\varepsilon_F$) decreases; the MPD, thermal and other properties change. The model of q-bit is proposed and based on helicoid nanodomains