What is the ruling regarding a wife remaining married to her husband despite her repeated defiance (nushooz), her refusal to serve him, and her leaving the home without his permission; and is it permissible for the husband to continue spending on her despite all of this?

If a wife is disobedient (nashiz) - unless she is pregnant - she is not entitled to maintenance. If attempts at reconciliation fail with her, she can be left in limbo without maintenance until she abandons her disobedience, or one can refrain from divorcing her until she waives the dower or part of it.