What is the ruling on a girl going out with her paternal or maternal uncle to fulfill her needs when her father or brothers do not do so, and is her father's permission required for this? And what is the ruling on this after the father's death, with brothers who do not fulfill her needs?

It is more befitting for a woman to remain in her home and not to leave except out of necessity. She is permitted to leave when there is a need that no one else can fulfill, provided she adheres to the Islamic guidelines for going out: she must not be displaying her adornments (mutabarrijah) or wearing perfume (mutatayyibah). She is not required to be accompanied by a mahram (definition), nor is she required to seek permission from her father, if the place she is going to is safe. Otherwise, she must go out with one of her mahrams.