  A detailed study of $\alpha$-clusters decay is exhibited by incorporating
crucial microscopic nuclear structure information into the estimations of
half-life and preformation factor. For the first time, using the k-cross
validation approach, two semi-empirical formulas for (i) $\alpha$-decay
half-life and (ii) $\alpha$-particle preformation factor, are picked out and
subsequently modified by including shell, odd-nucleon blocking, and asymmetry
effects along with the usual dependence on $\alpha$-decay energy ($Q_{\alpha}$)
and angular momentum of $\alpha$-particle. Both the formulas are fitted for the
two different regions separated by neutron number N$=$126, as from the
experimental systematics the role of N$=$126 shell closure is found decisive in
determining the trends of $Q_{\alpha}$, $\alpha$-decay half-life, and
$\alpha$-particle preformation factor. It is found that the inclusion of the
above-mentioned degrees of freedom significantly reduces the errors in the
estimations when compared with several other similar modified/refitted
semi-empirical relations indicating the robustness of the proposed formulas.
The predictions of $\alpha$-decay half-life throughout the periodic chart have
been made including the unknown territory, future probable decay chain of
self-conjugate nucleus $^{112}$Ba terminated on $^{100}$Sn, decay chain of
$^{208}$Pa through new isotope $^{204}$Ac as well as decay chains of awaiting
superheavy nuclei $^{298}$Og and $^{299}$120.
