Is it permissible for a daughter to dispose of her sick father's money and buy gifts from it for her siblings and their children after her father's absolute permission? And is it obligatory for her to inform him of every financial transaction or charity she disburses from his money?

It is not permissible for a daughter to donate or give charity from her father's money on behalf of her deceased mother unless she has explicit permission from him; for general authorization does not include donation and charity. If she disposes of the money without his permission, then the money is accounted as hers and not from her father's property. Also, if the father loses his mental faculties, the authorization becomes void, and the agent is not entitled to act at that point.