Yes, all your info is correct. She can use room and board as a qualified expense for the ESA distribution. She can only count the months she was enrolled in class. The amount she can claim is limited to the lesser of her actual cost or the school's room and board allowance for attendance (essentially what the school charges on campus students). As a practical matter, "everybody" uses the school's R&B charge.
Books and computers are also qualified expenses for the ESA (but not for the LLC),
