Is the daughter entitled to claim a sum of money saved in her name by her father, and is she entitled to insist on requesting it if the father refuses, knowing that she is in dire need of the sum and it is not being used?

You do not have the right to demand from your father the money he saves for you, because it remains in his possession and ownership of the money does not transfer to you except by taking possession of it during your father's lifetime. However, there is no harm in presenting your needs to your father and explaining your situation to him.