Incorrect. The trigeminal nerve provides general sensation from the anterior 2/3rd of the tongue via the lingual nerve (branch from the main V3 mandibular division).  

Incorrect. The facial nerve provides gustatory sensation from the anterior 2/3rd of the tongue via the chorda tympani nerve which joins to the lingual nerve en route to the tongue.

Incorrect. The vestibulocochlear nerve provides sensory information from the vestibular apparatus (balance) and the cochlear (auditory).  

Correct! This nerve provides general and special (taste) sensation to the tongue and pharynx. There is one muscle (stylopharyngeus  m.) innervated by the glossopharyngeal nerve, but this motor role is limited and the nerve primary role is sensory to the posterior tongue/pharynx.

The course of the nerve takes it in close proximity to the deep (lateral) aspect of the palatine tonsils. Post surgical inflammation could impede nerve function transiently until the inflammation subsides.

An excessively deep dissection during tonsillectomy could directly injure the nerve. This is rare as that depth is uncommon to rare to need to perform a radical tonsillectomy dissection into the tonsil base.

Incorrect. The vagus nerve is the primary motor nerve to the pharynx innervating the constrictor muscles and the salpingoparyngeus & palatopharynggeus muscles. Primarily involved in motor control of swallowing with limited sensory roles in the area.

Incorrect. The accessory nerve provides motor control of the sternocleidomastoid and trapezius muscles. This is purely a motor nerve with no sensory role and not role in oral/pharynx of any kind.

Incorrect. The hypoglossal nerve innervates the bulk of musculature controlling the tongue. This is purely a motor nerve with no sensory role.