1. To answer your first question - there is a rule of law that the donee of a Power of Attorney, such as your sister, should not profit from their position as holder of the Power. Any transaction under which the donee of a Power of Attorney such as your sister benefits from her Power can be set aside in legal action by the donor of the power or his executor on his death, or by any other interested person such as yourself.
2. Accordingly, your sister should not be using her Power of Attorney to pay off her mortgage irrespective of whatever financial recompense she might give your father. This is an unlawful use of a Power of Attorney.
3. Whilst a Deed of Trust is effective to pass any interest in your sister's house back to your father's estate upon death, the whole transaction is suspect and should not happen. The donee of a a power of Attorney such as your sister should not be meddling in your father's financial affairs to benefit herself.
I am very satisfied with this answer which confirms my opinion. Very clear and concise