Is the son obligated to pay the price of the apartment that the father sold to help him with his debts, knowing that the father did not inform the son or the rest of the family that it was a debt upon him, while he informed everyone of another agreement concerning another part of the inheritance?

If a father gives his son money to pay off his debts without explicitly stating that it is a loan, the default assumption is that it is a gift. Favoring some children in giving, due to need, is permissible according to some scholars.

However, if it is established that the father told your sisters that this money was a loan, then it must be returned to the estate to be distributed among the heirs. Certainty is not dispelled by doubt, and your not knowing whether this was his final opinion does not matter.