Is it sufficient to give Zakat al-Fitr belatedly for a past year, while having given charity to oneself and one's dependents, and then to give it in the following year for both years?

If your friend found what exceeds his needs and the needs of those he supports for the day and night of Eid, he must give out zakat al-fitr to its rightful recipients and not delay it beyond the day of Eid. By delaying it, he has sinned and must repent and give out the charity. If he has already given it out, then he is absolved. It is not permissible to give zakat al-fitr to those whose maintenance is obligatory upon the giver, because they are rich by virtue of this maintenance. He could have paid the zakat to those who ask for it if he was reasonably certain of their entitlement.