Is the mother's prayer valid or must it be repeated if she prayed with tayammum while in bed, in a state of exhaustion and semi-unconsciousness for two days after surgery, and how does she make up for the missed prayers?

If the mother is not aware of what she is saying in her prayer, she must immediately make up the missed prayers in their proper order and not delay the making up.

If she is aware, she must perform ablution (Wudu') with water. If she is unable to use water due to illness or similar reason, she is permitted to perform Tayammum with pure dust that adheres to the hand. If she performs Tayammum with something other than dust, or performs Tayammum while able to use water, she must make up the prayer.