Pain is never normal, but rather a sign that something is amiss. If, as the previous answer suggests, you are growing, you could feel some aches but it shouldn't be painful. Pain in the knee could be from an injury you are not aware of having (sports or a slip) which might go away. All persistent pain needs to be told to a doctor.
If you are at the age where you experience growing pains, yes... They often happen at night because thats when your body grows the most is when you sleep
Not necessarily, it almost sounds like a mild case of restless leg syndrome is it only in the knees?