Is it possible for young people in their 20s or 30s to get Alzheimer's disease?

Very unlikely. Alzheimer's disease is not the only cause of dementia the typical alzheimer disease is highly unlikely in the age group you mention.
Possible not likely. It would be very unusual for someone in his/her 20s or 30s to get Alzheimer's disease. However, there are many reasons for memory issues in someone that age--vitamin deficiency, alcohol, hypothyroidism, head trauma, drugs (Rx or other), etc. If you are worried, I would talk with your primary or go to a neurologist. Take care and stay healthy!
Yes. Less likely though. Other causes or diseases have to be considered.