The hypoglossal nerve is the twelfth cranial nerve and innervates the tongue muscles. If there is a unilateral injury to the hypoglossal nerve, the tongue will deviate towards the side of injury. In this question there is concern for an injury to the left hypoglossal nerve so you would expect tongue deviation to the left.
Horner's syndrome is characterized by ptosis, anhidrosis, miosis, enophthalmos and loss of ciliospinal reflex on the affected side of the face. It is caused by injury to the sympathetic chain, which can occur during an anterior approach to the neck.
The recurrent (inferior) laryngeal nerve is a branch of the vagus nerve (tenth cranial nerve) that supplies motor function and sensation to the larynx. A unilateral injury to the recurrent laryngeal nerve may lead to voice changes including hoarseness. Bilateral nerve damage can result in breathing difficulties and aphonia, the inability to speak.