Is it permissible to fast for an expiation of an oath for someone who does not possess money, given that the father is able to spend, and is it valid to refuse to accept money from the father or relatives to pay the expiation and suffice with fasting?

Fasting is not sufficient for expiation of an oath except after being unable to feed, clothe, or free a slave. If you do not have enough money to pay the expiation, then fasting three days will suffice for you. You are not obligated to ask your father for money or to accept what would expiate your oath from anyone, because of the obligation and favor that would be upon you. Fasting will be sufficient for you in this case, even if the giver were your father.