Is it permissible to prepare food and send it to the family of the deceased on the morning of their daughter's death with the intention of giving charity on behalf of the deceased?

What your father did by preparing food for the household of the deceased is permissible, and indeed, it is from the Sunnah, based on the Prophet's (peace and blessings be upon him) saying: "Prepare food for Ja'far's family, for that which occupies them has come to them."

The scholars have agreed that charity given on behalf of the deceased is accepted, based on the Prophet's (peace and blessings be upon him) response to someone who asked him: "My mother died suddenly, and I think if she had spoken, she would have given charity. Will she have a reward if I give charity on her behalf?" He said: "Yes."