What is the ruling of Islamic law regarding a working and capable son's refusal to contribute to household expenses, and is the father obliged to cover all of his expenses after his marriage and continued residence with him?

The wealthy and affluent son is not entitled to financial support from his father. The obligation of financial support ceases when the children reach maturity and are capable of earning. If the father gives him money willingly from his own wealth, that is good, and it is considered a recommended and desirable act, not an obligation. It is permissible to borrow from banks if the loan is without interest. However, if it involves interest, then it is usury (riba), which is forbidden.