Are people with dementia still wise?

Yes. Yes they are still wise in many areas. Memory loss and confusion typically start with difficulty in forming new memories and gradually progress into other areas. Factual knowledge is retrieved in a different manner that personal memories. The degree of dementia determines which areas are most profoundly affected so a person can be wise but unable to identify familiar individuals.
It Depends. Being wise refers to an ability to discern or judge what is true or right, and implies common sense and good judgment. While some likely are wise, and are able to discern or judge what is true or right, and have good common sense and judgment, others may no longer exhibit this quality. The presence or absence of “being wise” may vary on the type and severity of the dementia, and on other factors.
Memory loss. Is not an all or nothing thing, so yes, some dementia patients are wise, particularly early in the illness.
Maybe. They may still be wise though they may be unable to communicate their wisdom.