Is it permissible to give Zakat to a retired father who lives with his divorced daughter, and she provides for the household? And is it forbidden for the daughter to act out and be aggressive towards her parents during their quarrels, even though advice does not benefit them?

It is not permissible to give zakat to poor or retired parents, because their maintenance is obligatory upon their children, and zakat is not given to those whose maintenance is obligatory. It is obligatory to honor, respect, and be kind to one's parents, and not to raise one's voice at them, as Allah عز وجل enjoined in His Book.