Is there a test I can do to check my acoustic ceiling for asbestos? If it asbestos then can I remove it legally by myself?

I have an old steel soap dish that was installed when my home was built (1981). The builder appeared to have simply cut a 4" square in the drywall, slid the soap dish in the hole then tiled around it. I can't tell what material they used to keep it in the wall (a fellow at Ace Harware reckons they just put mortar on the back of it and around the edges). To make matters worse, the soap dish doesn't fit flush up against the tile around it, so I can't just apply caul around it. Do you have any suggestions how I can reinstall the soap dish without having to cut cut out part of the wall and installing new green board and re-tiling? I basically have just a hole (nothing behind it) in the wall right now..... Thank you!