What should one do if they find an insect with a broken leg due to being stepped on; should they kill it or leave it, especially if it is a "praying mantis" or an ant?

There is no harm in killing an injured insect or animal that is suffering; it must be relieved of its suffering by the best possible means of killing. There is a prohibition against killing ants unless they are harmful or bothersome. Killing it here is to relieve it of suffering, meaning to slaughter it, not to intentionally kill it. It is permissible for the owner to slaughter an animal that he cannot feed or sell.