Why do we recite the kaddish after the death of a loved one as well as what is the significance of saying the kaddish, lastly why is it limited to only those that have lost a parent or sibling?
Kaddish is said not after the death of "a loved one" but after the death of a person's mother or father (or brother or sister- if there is no son or father to say the kaddish). The kaddish sanctifies G-d's name and- said by a son (who, in a sense, is a continuation of his parents) in the memory of his parent- acts to offset any act of desecration that may have been caused by the deceased. Also, because the mourner, in his anguish might come to question the justice of G-d's providence, the saying of the kaddish reenforces his faith (Gesher Hachayyim I ch. 30, 4 a).