Is the dog impure, is it permissible to keep dogs, and what is the wisdom behind the presence of a dog with the Companions of the Cave? Did the Prophet keep a cat? And is a black dog or a black cat a devil? And what is the ruling on killing a black dog?

It has not been established that the Messenger of Allah, peace and blessings be upon him, adopted a cat or took one with him to prayer. Raising cats is permissible. As for the black dog, it is a devil according to the text of the hadith, and this ruling is sufficient in the Sunnah and does not need to be mentioned in the Qur'an.