Is it permissible for my father to perform tayammum for prayer, given his health conditions that prevent him from moving and reaching water for ablution, and his inability to stand?

We ask Allah to grant your father healing. He is obligated to perform ritual purity to the best of his ability, based on the Almighty's saying: "So fear Allah as much as you are able." He is not permitted to perform tayammum if he is able to use water with assistance. If he is unable to use water and finds no one to assist him, he should wash what he can and perform tayammum for the rest.