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.