Using Composition and Implementation in state Design Pattern

I read this link enter link description here, to learn State Desing Patern.

interface class:

   public interface State {
        void doAction();
    }

onState class:

public class TVStartState implements State {

@Override
public void doAction() {
    System.out.println("TV is turned ON");
}

}

offState:

public class TVStopState implements State {

@Override
public void doAction() {
    System.out.println("TV is turned OFF");
}

}

TvContext Class:

public class TVContext implements State {

private State tvState;

public void setState(State state) {
    this.tvState=state;
}

public State getState() {
    return this.tvState;
}

@Override
public void doAction() {
    this.tvState.doAction();
}

}

test Class :

public static void main(String[] args) {
    TVContext context = new TVContext();
    State tvStartState = new TVStartState();
    State tvStopState = new TVStopState();

    context.setState(tvStartState);
    context.doAction();


    context.setState(tvStopState);
    context.doAction();

}

Now I have two questions :

1- why TVContext Class implements State and has Composition toghether ? is a bug in OO ? because for example Cat inherits from Animal class and has_a animal together (in this case).

2-If The final programmer in this TestClass pass context to context.setState() instead tvStartState or tvStopState , Program successfully compiles but error in run_time.

For the second question in State Design Pattern, instead of inheritance, same name method can be used. but int Decoration Design Pattern not.