Is it permissible to eat from food bought by a relative of mine with money she took from her father without his knowledge, and is it permissible to use her possessions?

The maintenance of an unmarried daughter who has no wealth is obligatory upon her father. If the father withholds her maintenance, she is entitled to take what suffices her from his wealth, in a reasonable manner, without excess. Whatever exceeds her needs, she is obligated to return. There is no harm in eating from her food or accepting her gift, because what is forbidden is only what exceeds her needs, and dealing with mixed wealth is permissible.