All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad is His slave and Messenger.
Your statement ‘Feeding ten poor people or clothing them must be from one’s own money’, is not correct. Rather, if you ask someone to pay this on your behalf, or that someone volunteers to pay it for you and you give him permission to do so, then this is sufficient and acceptable, because expiating is an act of worship and the intention is required for this act to be valid.
Similarly, if your father gives you pocket money and you save from it and pay the expiation, then this is sufficient from you. Besides, if you own any item which will cover the price of the expiation and you can sell it without facing any difficulty, then you must sell it in order to get the price of the expiation, and you should not shift to expiate by fasting while being able to expiate with something else.
For more benefit on how to expiate for breaking an oath, please refer to Fatwa 84596.
It should be mentioned that expiating for your oath does not mean underestimating the seriousness and gravity of masturbation, because it is a forbidden and harmful habit. Therefore, you should stop doing it and stay away from the reasons which lead to it. For more benefit on the ruling on masturbation and how to treat it, please refer to Fatwa 81150.
What you are required to do now is to repent to Allaah and seek His Forgiveness from your sins, and you should follow the sins with good deeds in order to wipe them out.
As regards your supplication about corresponding with your friend, it might be that what happened is due to your supplication being answered. It was not correct to supplicate with such a supplication; rather, you should supplicate with what benefits you in your worldly life and your Hereafter, like supplicating Allaah for pardon and well-being, for guidance and for protecting you from the evil which is within yourself, for purifying your heart, keeping your private parts chaste and so forth.
Therefore, if your friend is a pious person, and you want to correspond with him in what benefits you in this life and the Hereafter, then you should supplicate Allaah to reconcile between you and make your friendship in what benefits you in religious and worldly matters last longer, and you should not stop corresponding with him even if he delays answering you, because it might be that he has an excuse but you do not know.
Allaah Knows best.