Is what a father spent from trusts deposited with him considered a debt upon him, and is the son obligated to repay it after the father's death, especially with the father's doubt about a remaining amount that was not repaid to one of the deceased depositors?

The fundamental principle is the presumption of innocence from liability. A trust (wadi'ah) is not established by mere doubt; rather, it requires certain knowledge or a strong presumption. It is more prudent to ask the heirs of the deceased. You are not obligated to repay your father's debt except as an act of kindness. Your father's disposal of people's trusts without their permission is impermissible and considered a betrayal and a guarantee of liability. As for borrowing from a trust, it is permissible only if the trustee knows with a certainty that gives him peace of mind that the owner of the money is content with it; otherwise, it is not permissible.