There are many missing links in reaching a proper diagnosis of your mother's illness.
You may need to elaborate her headaches like its exact duration of onset, location, timing and duration of each episode, trigger factors if any, relieving factors if any, severity etc.
Duration of onset of severe headache is one month as u said. It calls for further investigation to the cause and raises the suspicion of organic brain disorder.
Alzheimer's Disease is a common old age related degenerative brain Disorder but it usually starts after 60 years and gross brain changes only become evident after many years of illness. Alzheimer's disease has symptoms of memory loss; thinking process, decision making and understanding problems along with psychiatric symptoms.
As control of blood pressure fails to correct headache therefore it is likely that raised blood pressure is a response to headache than its cause.
Evaluation by a neurophysician seems mandatory to assess the findings of dilated CSF spaces and its relation to Headache in order to find out any obstructive pathology of CSF channels.
She can take a balanced diet including fair amount of proteins, vegetables, fruits etc and some multivitamin supplement like Surbex-T or Multibionta for general well being although we do not have any specific brain cell tonics unfortunately. But let us investigate her case further before embarking upon final judgement.