Correct!  A mass effect (e.g. a tumor) in the pharynx could progressively be impinging on other structures causing sensations the patient is reporting.

Although tumors are not associated with halitosis, breath odor is sufficiently common that coincidental halitosis alongside a tumor is possible.

Incorrect. An infection of the tonsils (most common in palatine tonsils, but can occur with any of them) would be painful and likely result in elevated temperature. The absence of pain or fever indicates against infection as a source.  

Incorrect. This is surgical removal of the tonsils. Most patients have knowledge of when they get this procedure.

Correct! The presence of tonsillolith stones may cause tickling sensations and is associated with hallitosis. These can be painless or can cause some mild sore throat through to dysphagia depending on the severity.

Incorrect. While the glossopharyngeal nerve serves as the primary sensory nerve of the posterior oral cavity, a paralysis would be a diminishment of sensation and motor function. 

There are neurological conditions that cause parathesia (abnormal sensation akin to tingling, pins and needles, or numbness), dysesthesia (more intense aberrant sensation including pain, itching, stinging, tingling sensation), and hyperesthesia (increased sensitivity to touch or pain).

Incorrect. A perforation would most likely be painful and associated with dysphagia.