Sorry to hear of your diagnosis. I am 3 years post surgery for 1.5 AN, deaf in my left ear and doing well. Before diagnosis I too had experienced the very same symptoms, tinnitus, headache, unsteadiness, extreme exhaustion even if I had a couple good nights sleep, facial symptoms same as yours that progressed to achy feeling when I smiled then drooling, fullness in my left ear with hearing loss. It was an ENT (2nd one) that finally ordered tests that showed my AN. I agree with your surgeon (sounds like he's educated in AN's), even 4mm tumor can cause these symptoms. I've said it before, "Size doesn't matter."
When this tumor is growing it can cause symptoms of vertigo (feeling of being pushed in one direction, like being on a tiltawhirl ride), different from dizziness (room spins) and the eyes are constantly working to keep you centered. This is one cause of exhaustion--stimulation overload. Headaches are a symptom of brain tumor (AN's don't grow from the brain, but nerves that connect to the brain stem). Depending on where your tumor sits on the nerve your symptoms will vary, even if you have a relatively small tumor. Some people's only complaint is fullness in the ear and their tumor can be medium to large. Lack of sleep does enhance symptoms that is why it is good idea to get as many good nights sleep as you can. I use 5 mgs of melatonin and this works for me, others must use something stronger such as Ambien.
Each of us have similar symptoms, each of us choose different treatments (there is no right decision), and each of us go down the very same road you are now on, learning all there is (not much known--yet) regarding your tumor and treatment. Education is "key", bringing tape recorder to any and all doctors appointments is very helpful as one tends to forget due to the stress of knowing you have a brain tumor, reading any and all information provided by the ANA is very helpful, dealing with doctors specifically trained (hundreds if not thousands of procedures under belt) on AN's, and finally knowing you are not alone as we are here for you and any questions you may have now and in the future!