Is it permissible for a father to give the zakat from his wealth to his indebted (insolvent) son, and then take it back from him?

Scholars have differed regarding the permissibility of giving Zakat to a debtor and then taking it back from him in repayment of the debt. Some disliked this if it involved a stratagem to reclaim the money, while others permitted it if there was no prior collusion for its return.

As for a father giving his Zakat to his son, this is not permissible unless the son's maintenance obligation has fallen from the father, such as when the son becomes an adult capable of earning.

Regarding your father's friend who gave him money to distribute as Zakat: If you mean that he gave you this money as Zakat from that fund, then scholars have disliked the agent singling out his relative with what he was entrusted to distribute from Zakat.