The reason nicotine is a poison is because a) it is very toxic in pure form b) because it is a pesticide c) because the reason plants make nicotine is to kill insects. It is a poison, the same way that snakes make poison to kill, plants make nicotine to stop them being eaten by insects.
It is a drug yes because it has psychoactive effects.
It is also a poison.
Incorrect, it is in plants to discourage them from eating the plant, not to kill the insect.