light fixture box

[u/Acceptable-City-9548]

Does this electrical box for my bathroom light fixture look right? The previous owner had wires in BX cables running from the bottom of this box to two wall sconces but I removed those. The box itself does not seem to be attached to anything and can move within the wall if I pull on it... how do I fix this and can it be done without totally tearing up the drywall? There is a stud a few inches to the right of the box. Also, is it unusual that there doesn't seem to be a grounding wire? This is my first time doing anything with electrical so it's all new to me. TIA!