Over the last few years we have developed the multi-reference density functional theory (DFT) involving the isospin- and angular-momentum projections of a single Slater determinant. The model, dubbed below static, was specifically designed to treat rigorously the conserved rotational symmetry and, at the same time, tackle the explicit breaking of the isospin symmetry resulting from a subtle balance between the long-range isospin-symmetry-breaking Coulomb field and short-range isospin-symmetry-conserving (predominantly) strong force. These unique features allowed us to calculate, in between, the isospin impurities in N~Z nuclei and isospin symmetry breaking corrections (ISB) to superallowed Fermi beta-decay matrix elements. Recently, we have extended the model to a variant (hereafter called dynamic) that allows for mixing of states that are projected from self-consistent Slater determinants representing low-lying (multi)particle-(multi)hole excitations. The states that are mixed have good angular momentum and, at the same time, include properly treated Coulomb isospin mixing. Hence, the extended model can be considered as a variant of the no core configuration-interaction approach, with two-body short-range (hadronic) and long-range (Coulomb) interactions treated on the same footing. It is based on a truncation scheme dictated by the self-consistent deformed Hartree-Fock (HF) solutions. The model can be used to calculate spectra, transitions, and beta-decay matrix elements in any nuclei, irrespective of their neutron- and proton-number parities. The aim of the talk is to introduce the theoretical frameworks of both the static and dynamic approaches and present selected applications. The applications will be focused on nuclei relevant to high-precision tests of the weak-interaction flavor-mixing sector of the Standard Model. In this context, we will present the results for ISB corrections to superallowed Fermi transitions and for the low-spin spectra in: 32S and 32Cl nuclei, in A=38 Ar, K, and Ca nuclei, and in 62Ga and 62Zn nuclei. In case of 62Zn the spectrum of 0+ states will be addressed. The 0+ states in this nucleus were reassigned in a recent experiment, and are now posing a challenge to theory.