I believe the description of your mother's behavior would fit the symptoms of Alzheimer's, though I can't say one way or another about seizures. My father had times of clarity and then times when he was incoherent or agitated, and it would cycle, usually due to an underlying infection. His disease affected his organs, causing infections and ramping up the dementia until it was under control with antibiotics. Whenever my father was having an episode where he wasn't acting like himself, his eyes would be glazed over.
As to your question regarding testing - has your mother been evaluated by a neurologist? From the Alzheimer's Association:
"There is no single test that proves a person has Alzheimer's. A diagnosis is made through a complete assessment that considers all possible causes."
56 yr. old--CD over 44 yr. Hemi-colectomy '01; spinal cord injury '01; fistulae since '97; enteropathic arthritis, chronic pain, muscle spasms, scoliosis, rotator cuff injuries