السلام عليكم ورحمة الله وبركاته AhsanAllahu ilaykum Can a niqabi go out and do things like play badminton with her family for example? جَزَاكَ ٱللَّٰهُ خَيْرًا

Yes, if she is covered and it is away from the sight of non mahram men, and Imam Ibn Baz said sport among women in a place men do not see and do not mix in does no harm. If it is where non mahram men see her, he said it is not allowed.