Is it permissible to eat from a broken or cracked dish, and what is the wisdom behind killing crows even though they punish each other by Allah's law?

It is permissible to eat from a broken dish and to use it, but it is disliked to drink from the chipped part of a cup or vessel, due to the prohibition of the Prophet (peace and blessings be upon him) against that. As for the crow, it is killed because it is one of the five noxious animals (al-fawasiq al-khams) that may be killed both inside and outside the Haram (sacred precinct), due to its harmfulness and corrupting nature.