Unfortunately it has not yet been covered in the course, although it is the normal way to say 'were sleeping'. It is used for continuous states, e.g. lying, standing, as opposed to the act of moving into a lying or standing position or going to sleep.
It is a compulsory contraction of *an an 'in their' so it literally means
They will not be in their sleeping tonight.
You will have to learn separate words for 'in my', 'in your', etc.
Yet another arbitrary “correct” response. Do please explain to me the difference between “they will not be sleeping tonight” (“correct”) and “they won’t be sleeping tonight”. This is generally a good package, but I’m getting really fed up with these arbitrary decisions. Remember that motivating learners is really important, especially when they are working on their own. I don’t suppose you employ a psychologist to advise you? It might be worth thinking about for the future.