Recent advancements, such as measurements of dipole polarizability and experiments involving parity-violating electron scattering on 48Ca (CREX) and 208Pb (PREX-II), have opened new perspectives for our understanding of nuclear en ergy density functionals (EDF). In particular, these advancements shed light on the isovector channel of the EDFs, which plays a pivotal role in determining properties related to symmetry energy and the thickness of the neutron skin in nuclei. Recently, a novel relativistic EDF DD-PCX has been developed based on point coupling in teraction, adjusted using not only the ground state properties of nuclei but also the properties of isoscalar giant monopole resonance and the dipole polarizability in 208Pb. The DD-PCX interaction describes well the nuclear ground state properties, including the thickness of the neutron skin, and provides reasonable descriptions of nuclear excited states. Furthermore, the symmetry energy and its slope are found to be consistent with previous studies. Moreover, by applying the relativistic EDF framework, the consequences of the CREX and PREX-II electron scattering data have been investigated for the symmetry energy of nuclear matter and the isovector properties of finite nuclei, such as neutron skin thickness and dipole polarizability. The weak-charge form factors extracted from the CREX and PREX-II experiments have been directly used to optimize the relativistic density-dependent point cou pling EDFs. Notably, the EDF derived from the CREX data yields substantially smaller values for parameters associated with symmetry energy, neutron skin thick ness, and dipole polarizability for both 48Ca and 208Pb, when compared to the EDF derived from the PREX-II data, as well as previously established EDFs. It has be come evident that the CREX and PREX-II experiments have not yielded consistent constraints for the isovector sector of the EDFs. Consequently, further theoretical investigations and experimental studies are required to clarify these discrepancies.