Am I sinful for requesting a landline telephone in my mother's name without her knowledge, using a general power of attorney from her, in order to pay off a previous debt, knowing that she would not have objected had she known, and she has since passed away? And what should I do now?

The agent is obligated not to exceed the limits of the agency, as it is based on trust, and exceeding it is considered a breach of trust. If the general agency includes requesting a phone in the name of the principal, then there is no harm. However, if it does not, then the agent has erred and must repent, pay the phone fees, and transfer the contract to his name.