Is anything incumbent upon you, and what should you do, after paying your sister the value of her inheritance share in your parents' house during their lifetime, and a contract was written to that effect to be implemented after their death, and your father has now passed away?

Discussing inheritance while both parents are alive is a sign of ill manners and an eagerness for their death. Death has no known appointed time, and a person's wealth remains their property until their demise.

Therefore, the contract made between you and your sister is void, and she must return the money you paid her.

After the father's death, your sister can sell her share of the inheritance. As for the living mother, your sister is not permitted to dispose of what she might inherit from her until after her death, because it is unknown who will die first.