Can young people get alzheimer's?

Not generally. Alzheimers disease is primarily a disease of older people. Development before 60 years of age is uncommon. In younger people some disorders can cause memory impairment such as can occur with trauma to the brain, childhood developmental disorders and drug abuse. Major depression can mimick dementia with slow thinking, lack of initiative, poor self care.
Yes thoug it's rare. Only about 3 to 5% of alzheimer's disease is of the hereditary variety. These tend to be the early onset people with alzheimer's disease.