Does this not use अपकी because the implied subject is "you"?
(And does that mean a "use your own thing!" command would take अपकी without an antecedent? Like would "read your own book!" be 'अपकी किताब पढ़ो!'?)
Neither Hindi nor English generally includes the subject (being commanded/told to do something) in the sentence.
Not sure about your second question, but I think so.