Is it permissible to eat from the food of a female relative who takes from her father's money more than she needs, and is it permissible to use her possessions?

If a father does not spend enough on his daughter to meet her needs according to what is customary, then it is permissible for her to take from his money without his permission only what she needs. Anything more than that is forbidden for her.

As for dealing with someone whose money is mixed with lawful (halal) and unlawful (haram) sources, such as eating their food or accepting their gift, it is permissible according to the preponderant opinion of scholars. The intention should be directed towards the permissible portion of their wealth, unless it is known that what they offer is specifically unlawful. The Prophet, peace and blessings be upon him, interacted with the Jews and ate their food despite their wealth being mixed with unlawful elements. This view has been adopted by many scholars, such as Al-Baghawi, Salman, Al-Hasan, Sa'id ibn Jubair, Mak'hul, Al-Zuhri, Shaykh Abdullah Aba Butayn, Al-Qalyubi, and Shaykh Ibn Baz.