Is it permissible to use the aforementioned method—which involves reciting specific verses and supplications a set number of times over water, then bathing with it, pouring it at the doorstep of the house, and giving charity—to attract a righteous husband? And is there any legal (Sharia) impediment in it or contradiction with prayer and belief in Allah's decree for the fulfillment of needs?

The Sharia has not specified particular supplications (adhkar) or a certain number for fulfilling needs. Specifying supplications with times or numbers for which there is no evidence in the Sharia is considered an innovation (bid'ah). A Muslim should restrict themselves to the adhkar and supplications that have been authentically transmitted. Informing people about one's need does not affect the delay in the answering of the supplication, for Allah may delay the answer for a wisdom He knows. Supplication is never lost; either it is answered swiftly, or it is stored for the Hereafter, or evil is averted by it.