Is it possible for children to show signs of schizophrenia before becoming a teenager?

Yes. Childhood onset schizophrenia, although rare, can emerge very early on in a child's life.
Yes, but rarely. Schizophrenia has been reported in children as young as 4-5 years old, but something about brain and hormonal changes after puberty make it much more common, with peak incidence at about age 18 years. Causes of schizophrenia remain unknown, as does why it can occur, though rarely, at much younger ages.