Do people with schizophrenia have any grasp of reality?

in psychology today we were watching a video on people with schizophrenia and this guy would constantly be pulling his hair up and say something that made sense and then go off into a whole different thing that was so strange it blew my mind like it seems that one second they are there mentally and the next theyre just off into their own world he literally said something about egg fusing with sperm then hes like "well thers two barriers and the first barrier breaks off like an electron breaking off a proton then the egg and sperm fuse like nuclear fusion, except its not nuclear fusion but it is" followed by him calling the psychologist "Mr. Greenteeth" and saying "I DONT NEED TO BE INSTITUTIONALIZED I KNOW YOUR JUST PLANNING TO TAKE ME OUT OF WHAT YOU GUYS CALL A NORMAL SOCIETY WHEN YOU DONT UNDERSTAND THAT IM NORMAL AND YOU ALL ARE JUST CRAZY!", so the real question i want to ask is do people with schizophrenia know that they are mentally unstable, are there any permanent treatmeants, whats going on in their brain that makes them act so weird(like what problems are they having with neurotransmitters i believe its D2?), and can someone with schizophrenia ever be completely normal, or atleast almost normal. thanks for your answers :) and im not trying to make fun of them i feel really bad for these warriors who have to suffer through schizophrenia i couldnt even imagine what its like but if you could answer my question it would be greatly appreciated, :) sorry if its long :(