Premarital sex, and is it the parents’ obligation to arrange marriage for their
    children?
Question

                I have heard that it is parents obligation
      to arrange for marraige of adult children and if they fail to do so, punishment for any
      sin committed by children is given to the parents. 
     Secondly, if anyone indulges in sex (not intercourse) with honest
      intentions to marry that person later, then is the sin committed by them forgiven? How bad
      is it for a muslim to do so?
Praise be to Allah.In answer to your second question, to say that it is permissible for a man
    to engage in a premarital physical relationship (even if it does not include intercourse)
    with a woman who is not permissible for him, claiming that he intends to marry her in the
    future, is total and utter nonsense. This can never be allowed by sharee’ah, and
    there can be no legitimate relationship until after the completion of a legal marriage
    contract according to Islamic law (i.e., nikaah).
I sent your first question to Shaykh ‘Abd-Allaah ibn ‘Abd
    al-Rahmaan al-Jibreen, and he wrote back to me with the following answer: 
Yes, it is a duty on the father to keep his children
    chaste by arranging their marriages, and spending on them and clothing them, if he is able
    to do so. If he is not able to, but the mother, grandfather or grandmother is able, it
    becomes that person’s duty to arrange the marriage. If the son cannot afford it but
    he has the ability to earn a living, it is his obligation to do so, in order to keep
    himself chaste. And Allaah knows best.