Stop servo when enter 0
From the code you posted it looks like you have the right idea but you've nested the 'IF' statements causing the check for '0' to only happen if you send two bytes and it will only go to 90deg when you send '10'.  The loop section should look more like:

if(Serial.available()){
    state = Serial.read();
    if(state == '1'){
           Make motor move;
    }else if(state == '0'){
           Make motor stop;
    }//end of elseif
}//end of if