Who should get to know the system of the company? - вопрос к подлежащему
You shouldn’t be a victim to their gossips by acting so silly, should you? - разделительный
Can it be really dangerous or safely if your take the first days in your office without much importance? - альтернативный
Does everybody like punctual people? - общий
What must you know? - специальный вопрос, ответ на него: You must know your responsibilities.