Ответ:

  1. B: While we were having a picnic, it started to rain.
  2. B: Alicia was painting a picture while her mum was cooking. В данном предложении ошибки нет; оба действия происходили одновременно. Если в учебнике требуется выбрать ошибку, вероятно, выделенная часть B должна быть исправлена на cooked только при понимании действия как завершённого события: Alicia was painting a picture when her mum cooked.
  3. B: Laura was taking off her coat and sat down.
  4. A: While we were on holiday, we spent most of our time sightseeing.
  5. A: Costa was listening to his iPod, so he didn’t hear the doorbell ring.