**Core Concept**
The patient's symptoms suggest a lesion affecting the spinal cord, specifically the lateral spinothalamic tract, which carries pain and temperature sensation, and the corticobulbar tract, which controls facial motor function.

**Why the Correct Answer is Right**
The corticobulbar tract is responsible for motor control of the facial muscles, and a lesion in this pathway would result in weakness of the face on the contralateral side. The lateral spinothalamic tract, on the other hand, carries pain and temperature sensation from the body, and a lesion in this pathway would result in loss of pain and temperature sensation on the contralateral side. The combination of facial weakness and loss of pain and temperature sensation in the opposite limbs suggests a lesion in the upper spinal cord, specifically at the level of the cervical spinal cord (C5-C6).

**Why Each Wrong Option is Incorrect**
* **Option A:** This option is incorrect because a lesion in the medulla oblongata would result in a different set of symptoms, including loss of cranial nerve function and respiratory compromise.
* **Option B:** This option is incorrect because a lesion in the pons would result in a different set of symptoms, including loss of cranial nerve function, ataxia, and dysarthria.
* **Option D:** This option is incorrect because a lesion in the lower spinal cord would result in loss of motor function and sensory loss in the lower limbs, not the upper limbs.

**Clinical Pearl / High-Yield Fact**
When evaluating a patient with a spinal cord lesion, it's essential to remember that the level of the lesion can be determined by the combination of motor and sensory deficits. A lesion in the upper spinal cord (C5-C6) would result in weakness of the arm and loss of pain and temperature sensation in the opposite limbs, while a lesion in the lower spinal cord would result in weakness of the legs and loss of pain and temperature sensation in the lower limbs.

**Correct Answer:** C.