A person with mental health problems can be aware of their behavior depending on the condition and its severity, though typically there will be some sort of “blind spot” where they aren’t cognizant of certain things they do or think. Treatment may involve bringing the person around to these blind spots and addressing them.
In my layman’s opinion, yes you can be a self-aware “insane” person. Though to be pedantic insanity is a catch-all term that’s too broad and vague, need more data.
P.S: I know you’re joking but i am inclined to take your request to discuss 
