Are inanimate objects and animals classified as believing and disbelieving? And must animals that the Prophet (peace be upon him) commanded to be killed be killed upon sight, or only when their harm is confirmed?

Animals and inanimate objects are not described as Muslim or disbelieving. It is recommended to kill geckos, and the reward for killing them is multiplied with the first blow, because this encourages hastening to kill them and take their lives. It is recommended to kill harmful insects such as mice, scorpions, snakes that are not "Awamir" (dwelling snakes), and generally any harmful insects. It is also recommended to kill the five "Fawasiq" (noxious creatures): the snake, the piebald crow, the mouse, the rabid dog, and the kite. As for house snakes, they should be warned before being killed. It is disliked to kill ants unless they cause severe harm.