Is it permissible for a woman to visit graves, and is her visit obligatory, and do the deceased await visitors to graves on Thursdays, and is a woman considered remiss in her duty towards her father if she does not visit his grave despite her consistent supplication for him, and what is the ruling of Islamic law on this, especially with the existence of fatwas prohibiting women from visiting graves?

A woman's visit to graves is not obligatory, and the preponderant view is that it is permissible under certain conditions. There is no evidence that the dead await Thursday. The deceased needs supplication and mercy more than a visit, and visiting reminds the living of the Hereafter. Therefore, it is not considered a shortcoming on her part if she stays in her home and increases her supplications for her father.