If a teenager says they have an imaginary friend, could this be a sign of schizophrenia or something?
It is unusual. Imaginary friends are a common phenomenon in children, up to about age 5-6. Most teens have a clear sense of "normal" behavior and would not likely have an imaginary friend. Let alone tell others. It the teen is doing well otherwise, probably no need for concern; but, it wouldn't hurt to ask what purpose the "friend" serves. And, if the teen is avoiding real friends, help might be needed.
No. If someone tells you they have an imaginary friend, then the person knows that the friend is imaginary. True hallucinations and delusions are very real to the person who is experiencing them.
Not Likely. An imaginary friend is not all that unusual. Problems such as schizophrenia usually involve a lack of awareness that such friends are not real.