No. Obsessions are not considered psychotic. Rather, they are recurrent and persistent thoughts that cause a lot of anxiety and distress.
Could be. I agree with dr. Smith that sexual obsession does not automatically indicate psychosis. However, there are people whose psychotic illnesses include sexual obsession. Consider john hinkley's assassination attempt on president reagan, said to be fueled by erotomanic obsession with jodie foster. In erotomania, the person delusionally believes that another person is secretly in love with him/her.
No. It is not.