Hi.. Your child is definitely low weight. We would expect a child of 4 yrs to be around 16 kg. A weight of 13 kg also would family within normal range. You mentioned height 3 ft 11 inches which comes to 119 cm . If your measurement is correct, then he  is too tall for his age. For 4 yrs average height is 103 cm and can be upto 111 cm. Most of the kids don't prefer home made food and want junk food. Parents must avoid encouraging outside food as much as possible. He  may be having Anemia (less blood). This can lead to irritability. Proper assessment of the child is needed before suggesting any advice.