How long does it take for a cats leg to heal from a sprain?

My cat fell and hurt her leg. She has been limping but shows major signs of improvement. I was wondering how long it may take for full recovery? Also, ever since she fell, she has not been using her litter box and even though she can climb inside the box, she refuses to use it. Is there a reason why she is not doing this and would the reason be related to her injury?