Must all debts be paid in full under a Chapter 13 plan?

No.  While priority debts, such as debts for domestic support obligations and taxes, and fully secured debts must be paid in full under a Chapter 13 plan, only an amount that the debtor can reasonably afford must be paid on most debts.  The unpaid balances of most debts that are not paid in full under a Chapter 13 plan are discharged upon the completion or termination of the plan.