  We update QCD calculations of $B \to \pi, K$ form factors at large hadronic
recoil by including the subleading-power corrections from the higher-twist
$B$-meson light-cone distribution amplitudes (LCDAs) up to the twist-six
accuracy and the strange-quark mass effects at leading-power in $\Lambda/m_b$
from the twist-two $B$-meson LCDA $\phi_B^{+}(\omega, \mu)$. The higher-twist
corrections from both the two-particle and three-particle $B$-meson LCDAs are
computed from the light-cone QCD sum rules (LCSR) at tree level. In particular,
we construct the local duality model for the twist-five and -six $B$-meson
LCDAs, in agreement with the corresponding asymptotic behaviours at small quark
and gluon momenta, employing the QCD sum rules in heavy quark effective theory
at leading order in $\alpha_s$. The strange quark mass effects in semileptonic
$B \to K$ form factors yield the leading-power contribution in the heavy quark
expansion, consistent with the power-counting analysis in soft-collinear
effective theory, and they are also computed from the LCSR approach due to the
appearance of the rapidity singularities. We further explore the
phenomenological aspects of the semileptonic $B \to \pi \ell \nu$ decays and
the rare exclusive processes $B \to K \nu \nu$, including the determination of
the CKM matrix element $|V_{ub}|$, the normalized differential $q^2$
distributions and precision observables defined by the ratios of branching
fractions for the above-mentioned two channels in the same intervals of $q^2$.
