HI,
Not sure if my info/experience is any help and certainly not medical advice as I am not a Dr.. but I just had AN surgery and had to have my facial nerve severed.. so I have facial paralysis and had to have a gold weight implant because eyelid does not close on it's own. I did not have any "issues" with that surgery, it was secondary to the AN surgery,, done 4 days later when they went in to graft a nerve to my facial nerve. I just have to use eye drops during the day and at night. The eyelid still does not close like when I am blinking, but does when I lay down.. no other real issues with it I guess.. It does bother me in windy situations and cold air, dusty etc.. and it is hard to remember not to rub that eyelid as you can feel the weight... not really sure about the MRI's usefulness in detecting nerve issue either,,,unless MRI is done to determine an AN which can involve facial nerve as mine did,, but you usually have some hearing indication or balance issues before facial issues with AN...like I said,, my opinions here,, not medical..
As for the grave's disease, seems like Dr would do thyroid blood testing to determine that issue.. it is hyperthyroid that leads to Grave's disease (overactive) ,, my husband has just been diagnosed with it, by simple blood work , testing T4 and T3 and TSH levels.. I had HYPOthyroid (underactive) several years ago causing thyroid nodules and eventually cancer so thyroid has been removed. I know the Grave's can impact your eyes too,, my husband's has not so far although he is early in diagnosis. His symptoms were extreme weight loss, fatigue and shaky hands and rapid heart beat.
Hope this helps any,, good luck in getting diagnosis and relief.. Jane