Question on cat

Question
My cat Kaiser is about 11 years old.  She is an indoor cat and  has recently started losing hair around her neck area and is patches on her belly.  She is also kind of oily all over.  I don't know if this has anything to do with it but a repair man broke a thermometer and spilled mercury shortly before I stared noticing these issues.  She is eating normally and other habits are normal as well,

Answer
I am not sure why you think the thermometer breaking and her losing hair are related as you didn't mention whether or not she was in the area before it was cleaned up or if she rolled in it.

Most alopecia (hair loss) is allergy related. These allergies can be food or more likely flea related.
They can also be hormonal. I would have her evaluated by a vet included blood work for mercury levels.