  We present a comprehensive analysis of weak transition form factors,
semileptonic decays, and nonleptonic decays of $B_c$ meson involving
pseudoscalar ($P$) and vector ($V$) meson for bottom-conserving and
bottom-changing decay modes. We employ self-consistent covariant light-front
quark model (CLFQM), termed as Type-II correspondence, to calculate the $B_c$
to $P(V)$ transition form factors. The Type-II correspondence in the CLF
approach gives self-consistent results associated with the $B^{(i)}_j$
functions, which vanish numerically after the replacement
$M^{\prime(\prime\prime)} \to M_0^{\prime(\prime\prime)}$ in traditional Type-I
correspondence, and the covariance of the matrix elements is also restored. We
investigate these effects on bottom conserving $B_c \to P(V)$ form factors that
have not yet been studied in CLFQM Type-II correspondence. In addition, we
quantify the implications of self-consistency propagating to weak decays
involving both bottom-conserving and bottom-changing $B_c$ transition form
factors. We use two different parameterizations, the usual three-parameter
function of $q^2$ and the model-independent $z$-series expansion, to establish
a clear understanding of $q^2$ dependence. Using the numerical values of the
form factors, we predict the branching ratios and other physical observables,
such as, forward-backward asymmetries, polarization fractions, etc., of the
semileptonic $B_c$ decays. We extend our analysis to predict the branching
ratios of two-body nonleptonic weak decays using the factorization hypothesis
in self-consistent CLFQM. We also compare our results with those of other
theoretical studies.
