Must I repeat the prayers I performed after the anesthetic wore off without ablution, without facing the Qibla, and without a head covering due to my health condition? If the answer is yes, how should they be repeated?

Firstly: The patient must make up the prayers he missed due to anesthesia immediately upon waking up.

Secondly: If the patient is unable to perform ablution (wudu') and cannot find anyone to help him, he should perform tayammum (definition) (dry ablution) using any available dust, such as from a wall or a bedspread if it has dust on it. If not, then the purification requirement is waived, and he should pray in his current state. The same applies to facing the Qiblah and covering the 'awrah (private parts); if he is able to do any of these, it is obligatory; otherwise, it is waived.

Thirdly: If the prayer was performed without purification or facing the Qiblah due to genuine inability and lack of assistance, then your prayer is valid and you are not required to repeat it. However, if you were able to perform tayammum or wudu' with assistance but neglected to do so, then you must repeat the prayers you performed.

Fourthly: It is obligatory to make up the missed prayers immediately and in their proper sequence, in one session as much as you are able. If that is difficult, then pray what you can and complete the rest afterwards.