Решение:
- We don't have to/don't need to cook tonight. We can get a pizza. (Отсутствие необходимости, так как есть альтернатива).
- She doesn't have to/doesn't need to get up early. She's on holiday. (Отсутствие необходимости).
- You must study harder or you are going to fail. (Сильная рекомендация или предупреждение).
- You must not drive faster than 120 km/h on the motorway. (Запрет, установленный правилом).
Ответ: 1. don't have to/don't need to; 2. doesn't have to/doesn't need to; 3. must; 4. must not.